Class X Mathematics

Chapter 8: Introduction to Trigonometry

Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.

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Chapter Overview

Welcome to Class X Mathematics: Introduction to Trigonometry. This chapter forms a core structural component of the math syllabus, designed to build analytical rigor and key formula models.

Use the detailed subtopic guide below to review standard definitions, key mathematical rules, and study guidelines.

Prerequisite Concepts

The Triangle and its PropertiesRatio and Proportion

About This Chapter

This comprehensive study guide for Introduction to Trigonometry is designed for Class X students following the CBSE and NCERT Mathematics curriculum. It covers 4 key subtopics including Trigonometric ratios of acute angles, Trigonometric values of specific angles (0, 30, 45, 60, 90), Ratios of complementary angles, and 1 more essential concepts. Whether you are preparing for school examinations, CBSE board exams, or competitive tests, this resource provides everything you need to build a strong conceptual foundation and achieve mastery.

The chapter includes 2 key formulas and equations, 1 fully worked step-by-step example problems, interactive practice exercises across 9 difficulty categories, timed mock quizzes, and downloadable worksheets. Each topic is explained with detailed concept definitions, mathematical representations, and expert study guidelines to help you understand not just the "how" but the "why" behind every formula and method.

Mathematics is a subject that rewards consistent practice and conceptual clarity over rote memorization. As you work through this chapter on Introduction to Trigonometry, focus on understanding the underlying principles first, then gradually increase problem difficulty. Use the practice sections to identify and strengthen weak areas, and refer to the common mistakes section to avoid the pitfalls that most students encounter.

What You'll Learn in This Chapter

By the end of studying Introduction to Trigonometry for Class X, you will have developed proficiency in the following learning outcomes as outlined by the NCERT syllabus:

State exact trig values for standard angles.

Prove basic trigonometric equalities.

Solve right-angled triangle missing values using trig ratios.

Prerequisites for This Chapter

Before studying Introduction to Trigonometry, make sure you are comfortable with the following prerequisite concepts. A strong foundation in these areas will help you understand new topics faster and solve problems more confidently:

The Triangle and its PropertiesRatio and Proportion

If any of these prerequisites feel unfamiliar, consider reviewing them first using the Related Chapters section at the bottom of this page. Building a solid base ensures you can tackle Introduction to Trigonometry with full confidence.

Real-World Applications of Introduction to Trigonometry

Students often wonder “Where will I use Introduction to Trigonometryin real life?” The answer is: everywhere. The mathematical concepts you learn in this chapter have practical applications across science, engineering, technology, medicine, finance, and everyday problem-solving. Here are some notable examples:

Height & Distance Measurement

Surveyors calculate the height of mountains, buildings, and towers using trigonometric ratios and angle measurements from the ground.

Sound Wave Analysis

Audio engineers model sound waves as sine functions to design speakers, concert halls, and noise-cancellation headphones.

Satellite Communication

Engineers calculate the optimal angle for satellite dish alignment using trigonometric principles for clear signal reception.

Medical Imaging (CT Scans)

CT scanners use trigonometric reconstruction algorithms to create detailed cross-sectional images of the human body.

Understanding the real-world relevance of Introduction to Trigonometry not only makes learning more engaging but also helps you appreciate how mathematical thinking is a superpower that opens doors in virtually every career path — from engineering and medicine to finance and technology.

Study Tips for Introduction to Trigonometry

Follow these expert study strategies to maximize your understanding and exam performance in this chapter. These tips are specifically tailored for the type of content covered in Introduction to Trigonometry:

📊

Master the Standard Value Table

Create a table of sin, cos, and tan values for 0°, 30°, 45°, 60°, and 90° and practice until you can recall them instantly. These values appear in almost every trigonometry problem.

🧭

Use ASTC Quadrant Rule

Remember "All Students Take Coffee" — All trig functions are positive in Q1, only Sine in Q2, only Tangent in Q3, only Cosine in Q4. This prevents sign errors in angle calculations.

🔺

Practice Identity Proofs Separately

Trigonometric identity proofs require a different skill set from numerical problems. Practice them separately, always working from the more complex side toward the simpler side.

Pro Tip: Consistency beats intensity. Studying Introduction to Trigonometry for 30 minutes daily is far more effective than cramming for 5 hours before the exam. Use the practice sections below to build muscle memory through regular problem-solving.

Detailed Topic Breakdown

Detailed Subtopics Study Guide

Review detailed conceptual explanations, mathematical equations, and guidelines for each subtopic in this chapter:

1Trigonometric ratios of acute angles

Concept Explanation

Trigonometric ratios express the relationship between the acute angles of a right-angled triangle and the ratios of its side lengths. The six basic ratios are Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent.

Mathematical Representation

\sin \theta = \frac{\text{Opp}}{\text{Hyp}}, \, \cos \theta = \frac{\text{Adj}}{\text{Hyp}}, \, \tan \theta = \frac{\text{Opp}}{\text{Adj}}, \, \csc \theta = \frac{1}{\sin \theta}, \, \sec \theta = \frac{1}{\cos \theta}, \, \text{cot} \theta = \frac{1}{\tan \theta}

Study Guideline: Remember the mnemonic 'SOH CAH TOA': Sine is Opposite/Hypotenuse, Cosine is Adjacent/Hypotenuse, Tangent is Opposite/Adjacent.

2Trigonometric values of specific angles (0, 30, 45, 60, 90)

Concept Explanation

Standard trigonometric values are derived from special right-angled triangles (45°-45°-90° and 30°-60°-90°). These values are highly used in mathematical evaluations and physics.

Mathematical Representation

\sin 30^\circ = \frac{1}{2}, \, \sin 45^\circ = \frac{1}{\sqrt{2}}, \, \sin 60^\circ = \frac{\sqrt{3}}{2}, \, \cos 30^\circ = \frac{\sqrt{3}}{2}, \, \tan 45^\circ = 1

Study Guideline: Memorize the sine values: 0, 1/2, 1/√2, √3/2, 1. Cosine values are the same sequence in reverse order.

3Ratios of complementary angles

Concept Explanation

Complementary angles are angles whose sum is 90 degrees. Trigonometric functions of complementary angles show co-function relationships: sine changes to cosine, tangent to cotangent, and secant to cosecant.

Mathematical Representation

\sin(90^\circ - \theta) = \cos\theta, \quad \tan(90^\circ - \theta) = \text{cot}\theta, \quad \sec(90^\circ - \theta) = \csc\theta

Study Guideline: Use co-function identities to simplify ratios of angles that sum to 90°, such as sin(53°)/cos(37°) = cos(37°)/cos(37°) = 1.

4Trigonometric identities: sin²+cos²=1

Concept Explanation

Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables. The three Pythagorean identities are fundamental to algebraic trigonometry.

Mathematical Representation

\sin^2\theta + \cos^2\theta = 1, \quad 1 + \tan^2\theta = \sec^2\theta, \quad 1 + \text{cot}^2\theta = \csc^2\theta

Study Guideline: When proving identity equations, express all ratios in terms of sine and cosine as a baseline starting strategy.

Scientific Calculator Active: A custom solver for the specific subtopics of this chapter is currently in development. In the meantime, please use our comprehensive Scientific Functions Calculator below to verify your study equations.

Scientific Functions Calculator

Solve trigonometric, exponential, logarithmic, and root functions for standard algebraic values.

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Value (X)45

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Function Output

0.71

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Deterministic Mathematical Simulation Engine • Verified Calculations

Date: 9/1/2026

Time: 8:47:03 AM

Scientific Functions Calculator

Solve trigonometric, exponential, logarithmic, and root functions for standard algebraic values.

1. Input Parameters

Parameter	Value	Unit
Value (X)	45	—
Function	sin	—

2. Calculated Results

Metric	Calculated Output
Function Output	0.707

Generated by NexProTools (www.nexprotools.com)

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Student Solver & Visualizer Guide

Real-time calculations

Step-by-step solving

1. Collect input parameters:

- operand1 = 45

- operation = sin

2. Feed parameters through standard algorithmic calculation methods.

3. Compile calculated results:

- calcResult = 0.7071

Student-friendly explanations

"This math utility processes input parameters using standard algebraic algorithms. By substituting variables into target formulas, the engine solves equations and computes results instantly with high arithmetic precision!"

Visual explanations

MATH SOLVER RUNNING:
 [Inputs] ──► [Mathematical Formula] ──► [Outputs]
  Processed elements successfully.

Class X CBSE Board Practice Questions

Review and solve 93 real Board paper questions from the 20 mock sample sets matching Introduction to Trigonometry.

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Sample Paper 01 | Question 2Section A (1 Mark)

If x tan 60°cos 60°= sin60°cot 60°, then x =

Sample Paper 01 | Question 7Section A (1 Mark)

sec θ when expressed in terms of cot θ, is equal to:

Sample Paper 01 | Question 13Section A (1 Mark)

For some data xl, x2, …….. xn with respective frequencies f1, f2, ..... fn, the value of 1 ( ) n i if x x -∑ is equal to:

Sample Paper 01 | Question 15Section A (1 Mark)

If cos (α + β) = 0, then value of cos 2 α β+( ) ( )( ) is equal to:

Sample Paper 01 | Question 21Section B (2 Marks)

Evaluate: 0 0 02 2 cos 45 sin 30 2 3 cos30+

Sample Paper 01 | Question 25Section B (2 Marks)

In the given figure, ABC is a triangle in which DE||BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, then find the value of x.

Sample Paper 01 | Question 27Section C (3 Marks)

Prove that: tan cot 1 sec cos1 cot 1 tan ecθ θ θ θθ θ+ = +- -

Sample Paper 02 | Question 2Section A (1 Mark)

If cosec A = 13/12, then the value of 2sin 3cos 4sin 9cos A A A A - -

Sample Paper 02 | Question 4Section A (1 Mark)

If sin 2A = 1 2 tan² 45° where A is an acute angle, then the value of A is

Sample Paper 02 | Question 8Section A (1 Mark)

If 3 sin θ - cos θ = 0 and 0° < θ < 90°, find the value of θ.

Sample Paper 02 | Question 24Section B (2 Marks)

If tan (A + B) = 3 and tan (A - B) = 1 3 ; 0° < A+B ≤ 90°; A > B, find A and B.

Sample Paper 03 | Question 2Section A (1 Mark)

In ΔABC, right angled at B, AB = 5 cm and sin C = 1/2. Determine the length of side A

Sample Paper 03 | Question 3Section A (1 Mark)

In the given figure, if AB = 14 cm, then the value of tan B is:

Sample Paper 03 | Question 4Section A (1 Mark)

If the distance between the points (4,p) and (1,0) is 5, then value of p is

Sample Paper 03 | Question 5Section A (1 Mark)

In the given figure, ∆ABC ~ ∆QPR. If AC = 6 cm, BC = 5 cm, QR = 3 cm and PR = x; then the value of x is:

Sample Paper 03 | Question 8Section A (1 Mark)

If x = a cos θ and y = b sin θ, then the value of b2x2 + a2y2 is

Sample Paper 03 | Question 20Section A (1 Mark)

Assertion (A): The value of y is 3, if the distance between the points P(2, -3) and Q(10, y) is 10. Reason (R): Distance between two points is given by 2 2 2 1 2 1( ) ( )x x y y- + -

Sample Paper 03 | Question 22Section B (2 Marks)

Simplify: 2 2 2 2 tan cot 1 tan 1 cot θ θ θ θ++ +

Sample Paper 03 | Question 30Section C (3 Marks)

If sec θ + tan θ = p, prove that sin θ = 2 2 1 1 p p - + .

Sample Paper 04 | Question 15Section A (1 Mark)

In ABC right angled at B, sin A = 7 25 , then the value of cos C is ………….

Sample Paper 04 | Question 16Section A (1 Mark)

If 5 tan θ = 4, then the value of 5sin 3cos 5sin 2cos θ θ θ θ - + is

Sample Paper 04 | Question 19Section A (1 Mark)

Assertion (A): The value of y is 3, if the distance between the points P(2, -3) and Q(10, y) is 10. Reason (R): Distance between two points is given by 2 2 2 1 2 1( ) ( )x x y y- + -

Sample Paper 05 | Question 7Section A (1 Mark)

If cosec A = 13/12, then the value of 2sin 3cos 4sin 9cos A A A A - -

Sample Paper 05 | Question 12Section A (1 Mark)

If tan θ = 1, then the value of sec θ + cosec θ is:

Sample Paper 05 | Question 13Section A (1 Mark)

Given that sin α = 1/2 and cos β = 1/2, then the value of (β - α) is

Sample Paper 05 | Question 20Section A (1 Mark)

Assertion (A): The value of y is 3, if the distance between the points P(2, -3) and Q(10, y) is 10. Reason (R): Distance between two points is given by 2 2 2 1 2 1( ) ( )x x y y- + -

Sample Paper 05 | Question 30Section C (3 Marks)

Prove that: 2 2cos sin 1 sin cos1 tan 1 cot θ θ θ θθ θ+ = +- -

Sample Paper 06 | Question 2Section A (1 Mark)

In the ∆ABC, DE ∥ BC and AD = 3x - 2, AE = 5x - 4, BD = 7x - 5, CE = 5x - 3, then find the value of x

Sample Paper 06 | Question 9Section A (1 Mark)

If the mean of the following distribution is 2.6, then the value of y is Variable (x) 1 2 3 4 5 Frequency 4 5 y 1 2

Sample Paper 06 | Question 12Section A (1 Mark)

The value of k for which the lines 5x + 7y = 3 and 15x + 21y = k coincide is:

Sample Paper 06 | Question 16Section A (1 Mark)

If 5 tan θ = 4, then the value of 5sin 3cos 5sin 2 cos θ θ θ θ - + is

Sample Paper 06 | Question 21Section B (2 Marks)

If 217x + 131y = 913, 131x + 217y = 827, then find the value of x and y

Sample Paper 06 | Question 22Section B (2 Marks)

If sin (A + B) = √3/2 and sin (A - B) = 1 2 , 0 ≤ A + B ≤ 90° and A > B, then find A and B.

Sample Paper 06 | Question 26Section C (3 Marks)

Prove that: sin cos 1 sec tansin cos 1 θ θ θ θθ θ - + = ++ -

Sample Paper 07 | Question 4Section A (1 Mark)

If C(1, -1) is the mid-point of the line segment AB joining points A(4, x) and B(- 2, 4), then value of x is :

Sample Paper 07 | Question 11Section A (1 Mark)

If one root of equation 4x2 - 2x+k-4=0 is reciprocal of the other. The value of k is:

Sample Paper 07 | Question 18Section A (1 Mark)

In ∆ ABC, right-angled at B, AC = 25 cm, BC = 7 cm. The value of tan C is:

Sample Paper 07 | Question 30Section C (3 Marks)

Prove that: 2 2 2 2 1 sin(tan sec ) (tan sec ) 2 1 sin AA A A A A ( ) ++ + - = ( ) -( )

Sample Paper 08 | Question 5Section A (1 Mark)

2 2 1 1 tan sinθ θ ( ) -( )( ) is equal to :

Sample Paper 08 | Question 12Section A (1 Mark)

If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:

Sample Paper 08 | Question 27Section C (3 Marks)

Prove that (cosec A - sin A)(sec A - cos A)(tan A + cot A) = 1

Sample Paper 09 | Question 9Section A (1 Mark)

If sinθ + cosθ = √2, then tanθ + cot θ =

Sample Paper 09 | Question 13Section A (1 Mark)

If value of each observation in a data is increased by 2, then median of the new data

Sample Paper 09 | Question 19Section A (1 Mark)

Assertion (A): If sin A = 1 3 (0° < A < 90°) , then the value of cos A is 2 2 3 Reason (R): For every angle θ, sin²θ + cos²θ = 1.

Sample Paper 09 | Question 28Section C (3 Marks)

Prove that: 3 3 2 2 tan cot sec cos 2sin cos1 tan 1 cot ecθ θ θ θ θ θθ θ+ = -+ +

Sample Paper 10 | Question 3Section A (1 Mark)

The value of 2 2 1sin 1 tanθ θ ( ) +( ) +( ) is :

Sample Paper 10 | Question 17Section A (1 Mark)

If 5 tanβ = 4, then 5sin 2 cos 5sin 2cos β β β β - =+

Sample Paper 10 | Question 21Section B (2 Marks)

If 49x + 51y = 499, 51x + 49y = 501, then find the value of x and y

Sample Paper 10 | Question 22Section B (2 Marks)

(a) If cos (A + B) = 1 2 and tan (A - B) = 1 3 , where 0 ≤ A + B ≤ 90°, then find the value of sec (2A - 3B).

Sample Paper 10 | Question 29Section C (3 Marks)

Prove that: 2 2 2 2 1 tan (1 tan ) 1 cot (1 cot ) A A A A ( ) + - =( ) + -( )

Sample Paper 10 | Question 30Section C (3 Marks)

Find the ratio in which the point 8 ,5 y( ) ( )( ) divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y.

Sample Paper 11 | Question 7Section A (1 Mark)

In the given figure, ∆ABC ~ ∆QPR. If AC = 6 cm, BC = 5 cm, QR = 3 cm and PR = x; then the value of x is:

Sample Paper 11 | Question 16Section A (1 Mark)

2 2 2 cos 1 sin sin θ θ θ- , in simplified form is:

Sample Paper 11 | Question 25Section B (2 Marks)

Evaluate: 2 0 2 0 2 0 2 0 2 0 5cos 60 4sec 30 tan 45 sin 30 cos 30 + - +

Sample Paper 11 | Question 26Section C (3 Marks)

Prove that: 3 3 sin 2sin tan2cos cos A A AA A - =-

Sample Paper 11 | Question 34Section D (5 Marks)

The monthly expenditure on milk in 200 families of a Housing Society is given below: Monthly Expenditure (in Rs.) 1000 - 1500 1500 - 2000 2000 - 2500 2500 - 3000 3000 - 3500 3500 - 4000 4000 - 4500 4500 - 5000 Number of families 24 40 33 x 30 22 16 7 Find the value of x and also, find the median and mean expenditure on milk.

Sample Paper 12 | Question 11Section A (1 Mark)

If is an acute angle and tan + cot = 2, then the value of sin3 + cos3 is

Sample Paper 12 | Question 19Section A (1 Mark)

Assertion (A): If x = 2 sin2θ and y = 2 cos2θ + 1 then the value of x + y = 3. Reason (R): For any value of θ, sin2θ + cos2θ = 1

Sample Paper 12 | Question 24Section B (2 Marks)

For what value of k, the following system of equations have infinite solutions: 2x - 3y = 7, (k + 2)x - (2k + 1)y = 3 (2k - 1)?

Sample Paper 13 | Question 9Section A (1 Mark)

The value of (sin 45° + cos 45°) is

Sample Paper 13 | Question 14Section A (1 Mark)

If tan θ = 1, then the value of sec θ + cosec θ is:

Sample Paper 13 | Question 16Section A (1 Mark)

If the mean of the following distribution is 2.6, then the value of y is Variable (x) 1 2 3 4 5 Frequency 4 5 y 1 2

Sample Paper 13 | Question 19Section A (1 Mark)

Assertion (A): The value of y is 3, if the distance between the points P(2, -3) and Q(10, y) is 10. Reason (R): Distance between two points is given by 2 2 2 1 2 1( ) ( )x x y y- + -

Sample Paper 13 | Question 26Section C (3 Marks)

If tan a bθ = , prove that 2 2 2 2 sin cos sin cos a b a b a b a b θ θ θ θ - - =+ +

Sample Paper 14 | Question 2Section A (1 Mark)

The mean and median of a distribution are 14 and 15, respectively. The value of the mode is:

Sample Paper 14 | Question 12Section A (1 Mark)

If for some angle θ, cot 2θ = 1 3 , then the value of cos3θ, where 3θ ≤ 90⁰, is

Sample Paper 14 | Question 13Section A (1 Mark)

In ∆ABC, right-angled at C, if tan A=1, then the value of 2sin A cos A is

Sample Paper 14 | Question 17Section A (1 Mark)

If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is

Sample Paper 14 | Question 21Section B (2 Marks)

In ABC, DE || AB. If AD = 2x, DC = x + 3 , BE = 2x - 1 and CE = x, then find the value of ‘x’ ⇒ 2x2 + 6x - x - 3 = 2x2 ⇒ 5x - 3 = 0 ⇒ x =

Sample Paper 14 | Question 22Section B (2 Marks)

If sin (A + B) = 1 and sin (A - B) = , 0 ≤ A + B ≤ 90° and A > B, then find A and B.

Sample Paper 14 | Question 29Section C (3 Marks)

Prove that sin cos 1 1 cos sin 1 sec tan θ θ θ θ θ θ - + =+ - -

Sample Paper 15 | Question 22Section B (2 Marks)

If sin(A + B) = 1 and cos(A - B) = √3/2, where 0° < A + B ≤ 90° and A > B, find the values of A and B.

Sample Paper 15 | Question 29Section C (3 Marks)

If sin θ + cos θ = √3, prove that tan θ + cot θ = 1.

Sample Paper 17 | Question 1Section A (1 Mark)

If cos θ + cos2 θ = 1, the value of sin2 θ + sin4 θ is :

Sample Paper 17 | Question 18Section A (1 Mark)

If cos A = 4/5, then the value of tan A is

Sample Paper 17 | Question 23Section B (2 Marks)

(a) If 2x + y = 13 and 4x - y = 17, find the value of (x - y).

Sample Paper 17 | Question 26Section C (3 Marks)

Prove that cos 1 sin 2sec1 sin cos A A AA A ++ =+

Sample Paper 18 | Question 1Section A (1 Mark)

If ½ is a root of the equation x2 + kx - 5/4 = 0, then the value of k is

Sample Paper 18 | Question 16Section A (1 Mark)

In the given figure, if ∆ABC ~ ∆QPR, then the value of x is :

Sample Paper 18 | Question 21Section B (2 Marks)

Evaluate: sin 30° cos 60° + cos 30° sin 60° - cot 45°

Sample Paper 18 | Question 27Section C (3 Marks)

If cosecθ + cotθ = p, then prove that 2 2 1cos 1 p pθ -= +

Sample Paper 19 | Question 2Section A (1 Mark)

In the figure given below, AD = 4 cm, BD = 3 cm and CB = 12 cm, then cot θ equals :

Sample Paper 19 | Question 10Section A (1 Mark)

If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:

Sample Paper 19 | Question 25Section B (2 Marks)

Evaluate: 0 0 0 0 cos 45 sin 60 sec30 cos 30ec + +

Sample Paper 19 | Question 28Section C (3 Marks)

Prove that: 3 3 sin 2sin tan2cos cos θ θ θθ θ - =-

Sample Paper 19 | Question 37Section E (4 Marks)

Tower Bridge is a Grade I listed combined bascule and suspension bridge in London, built between 1886 and 1894, designed by Horace Jones and engineered by John Wolfe Barry. The bridge is 800 feet (240 m) in length and consists of two bridge towers connected at the upper level by two horizontal walkways, and a central pair of bascules that can open to allow shipping. In this bridge, two towers of equal heights are standing opposite each other on either side of the road, which is 80 m wide. During summer holidays, Neeta visited the tower bridge. She stood at some point on the road between these towers. From that point between the towers on the road, the angles of elevation of the top of the towers was 60° and 30° respectively. (i) Find the distances of the point from the base of the towers where Neeta was standing while measuring the height. [2] (ii) Neeta used some applications of trigonometry she learned in her class to find the height of the towers without actually measuring them. What would be the height of the towers she would have calculated? [2] OR (ii) Find the distance between Neeta and top of tower AB? Also, Find the distance between Neeta and top tower CD?

Sample Paper 20 | Question 12Section A (1 Mark)

If 4 tan θ = 3, then the value of 4sin cos 4sin cos θ θ θ θ - + is

Sample Paper 20 | Question 15Section A (1 Mark)

In ΔABC, right angled at B, AB = 5 cm and sin C = 1/2. Determine the length of side A

Sample Paper 20 | Question 18Section A (1 Mark)

If sec A = 15/7 and A + B = 90°, find the value of cosec

Sample Paper 20 | Question 19Section A (1 Mark)

Assertion (A): The value of y is -6, for which the distance between the points P(2, -3) and Q(10, y) is 10. Reason (R): Distance between two given points A (x1, y1) and B (x2, y2) is given by AB = 2 2 2 1 2 1( ) ( )x x y y- + -

Sample Paper 20 | Question 21Section B (2 Marks)

In the given figure, find the value of x in terms of a, b and c.

Sample Paper 20 | Question 24Section B (2 Marks)

Find A and B, if sin (A + 2B) = √3/2 and cos (A + B) = 1/2.

Sample Paper 20 | Question 27Section C (3 Marks)

Prove that: sin cos 1 sec tansin cos 1 θ θ θ θθ θ - + = ++ - And: LHS = tan 1 sec tan 1 sec θ θ θ θ - + + - (Dividing numerator and denominator by cosθ) tan sec 1 tan 1 sec θ θ θ θ + -= + - 2 2tan sec (sec tan ) tan 1 sec θ θ θ θ θ θ + - -= + - (sec tan )(1 sec tan ) tan 1 sec θ θ θ θ θ θ + - += + - sec tanθ θ= + = RHS

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Chapter 8: Introduction to Trigonometry

Chapter Overview

Prerequisite Concepts

About This Chapter

What You'll Learn in This Chapter

Prerequisites for This Chapter

Real-World Applications of Introduction to Trigonometry

Height & Distance Measurement

Sound Wave Analysis

Satellite Communication

Medical Imaging (CT Scans)

Study Tips for Introduction to Trigonometry

Master the Standard Value Table

Use ASTC Quadrant Rule

Practice Identity Proofs Separately

Detailed Subtopics Study Guide

1Trigonometric ratios of acute angles

Concept Explanation

Mathematical Representation

2Trigonometric values of specific angles (0, 30, 45, 60, 90)

Concept Explanation

Mathematical Representation

3Ratios of complementary angles

Concept Explanation

Mathematical Representation

4Trigonometric identities: sin²+cos²=1

Concept Explanation

Mathematical Representation

Learning Outcomes

Sub-Topics Directory

Key Formulas & Equations

Pythagorean Identity

Tangent Ratio

Related Formulas from Adjacent Chapters

Distance Formula

Section Formula (Internal)

Height formula

Interactive Problem Solver

Scientific Functions Calculator

Adjust Inputs

Calculated ResultsCopy Output

NEXPROTOOLS COMPUTATIONAL REPORT

Scientific Functions Calculator

1. Input Parameters

2. Calculated Results

Student Solver & Visualizer Guide

Step-by-step solving

Student-friendly explanations

Visual explanations

Core Metrics

Focus Weak Areas

Select Practice Mode

Easy Practice

Medium Practice

Hard Practice

Timed Chapter Quiz

Interactive Worksheet

Chapter Syllabus Test

Prerequisite & Mixed Revision

Previous Year style (Board Exam)

Olympiad & JEE Challenge

Class X Quiz Challenge

Recommended Quizzes from Other Chapters

Mock Quiz: Introduction to Trigonometry

Adjacent Mock Quiz: Coordinate Geometry

Adjacent Mock Quiz: Some Applications of Trigonometry

Class X CBSE Board Practice Questions

Critical Mistakes to Avoid

!Degree vs Radian Confusion

!Incorrect Quadrant Signs

!Reciprocal Mistranslations

Revision Summary Cards

1Core Trig Functions

2Degrees & Radians

3Pythagorean Identity

4Prerequisites Checked

5Step-by-Step Checking

Frequently Asked Questions

Recommended Study Syllabus

Coordinate Geometry

Calculated Results

Calculated Results