Class 10 Maths Chapter 9 Introduction to Trigonometry Exercise 9.2 NCERT Solutions

NCERT Solutions for class 10 Maths Chapter 9 Exercise 9.2 is an important part of the CBSE Class 10 syllabus on Introduction to Trigonometry, focusing on trigonometric ratios for standard angles (0°, 30°, 45°, 60°, 90°) through evaluation, true/false, and application problems that frequently appear in board exams.

These NCERT Solutions are explained step by step to make it easier to follow each transformation and simplification. Practising these questions improves algebraic manipulation skills and builds confidence in solving identity-based problems9

NCERT Solutions for Class 10 Maths Chapter 9 Exercise 9.2

 1. Evaluate the following:

(i) sin 60° cos 30° + sin 30° cos 60°

(ii) 2 tan2 45° + cos2 30° – sin2 60

Solution:

(i) sin 60° cos 30° + sin 30° cos 60°

First, find the values of the given trigonometric ratios

sin 30° = 1/2

cos 30° = √3/2

sin 60° = 3/2

cos 60°= 1/2

Now, substitute the values in the given problem

sin 60° cos 30° + sin 30° cos 60° = √3/2 ×√3/2 + (1/2) ×(1/2 ) = 3/4+1/4 = 4/4 =1

(ii) 2 tan² 45° + cos² 30° – sin² 60

We know that the values of the trigonometric ratios are:

sin 60° = √3/2

cos 30° = √3/2

tan 45° = 1

Substitute the values in the given problem

2 tan² 45° + cos² 30° – sin² 60 = 2(1)² + (√3/2)²-(√3/2)²

2 tan² 45° + cos² 30° – sin² 60 = 2 + 0

2 tan² 45° + cos² 30° – sin² 60 = 2

(iii) cos 45°/(sec 30°+cosec 30°)

We know that,

cos 45° = 1/√2

sec 30° = 2/√3

cosec 30° = 2

Substituting the values, we get

Now, multiply both the numerator and denominator by √2 , we get

Therefore, cos 45°/(sec 30°+cosec 30°) = (3√2 – √6)/8

We know that,

sin 30° = 1/2

tan 45° = 1

cosec 60° = 2/√3

sec 30° = 2/√3

cos 60° = 1/2

cot 45° = 1

Substituting the values in the given problem, we get

We know that,

cos 60° = 1/2

sec 30° = 2/√3

tan 45° = 1

sin 30° = 1/2

cos 30° = √3/2

Now, substitute the values in the given problem, we get

(5cos²60° + 4sec²30° – tan²45°)/(sin² 30° + cos² 30°)

= 5(1/2)²+4(2/√3)²-1²/(1/2)²+(√3/2)²

 = (5/4+16/3-1)/(1/4+3/4)

= (15+64-12)/12/(4/4)

= 67/12

2. Choose the correct option and justify your choice :

(i) 2tan 30°/1+tan 2 30° = (A) sin 60°   (B) cos 60°  (C) tan 60°  (D) sin 30°

(ii) 1-tan  2 45°/1+tan 2 45° = (A) tan 90°   (B) 1    (C) sin 45°  (D) 0

(iii)  sin 2 A = 2 sin A is true when A = (A) 0°    (B) 30°  (C) 45°           (D) 60°

(iv) 2tan30°/1-tan 2 30° = (A) cos 60°   (B) sin 60°  (C) tan 60°  (D) sin 30°

Answer:

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

Answer:

 4. State whether the following are true or false. Justify your answer.

(i) sin (A + B) = sin A + sin B.

(ii) The value of sin θ increases as θ increases.

(iii) The value of cos θ increases as θ increases.

(iv) sin θ = cos θ for all values of θ.

(v) cot A is not defined for A = 0°.

Answer:

(i) False. Let A = 30° and B = 60°, then sin (A + B) = sin (30° + 60°) = sin 90° = 1 and, sin A + sin B = sin 30° + sin 60° = 1/2 + √3/2 = 1+√3/2

(ii) True. sin 0° = 0 sin 30° = 1/2 sin 45° = 1/√2 sin 60° = √3/2 sin  90° = 1 Thus the value of sin θ increases as θ increases.

(iii) False. cos 0° = 1 cos 30° = √3/2 cos 45° = 1/√2 cos 60° = 1/2 cos 90° = 0 Thus the value of cos θ decreases as θ increases.

(iv) True. cot A = cos A/sin A cot 0° = cos 0°/sin 0° = 1/0 = undefined.

How to Score Better in Class 10 Maths Exam?

Scoring well in Class 10 Maths requires clear concepts, regular practice, and a focus on accuracy and answer presentation. To score better, you should:

• Build Strong Concepts:

Focus on understanding concepts in Class 10 Maths instead of memorising steps, as this helps in solving application-based questions.

• Work on Weak Areas:

Focus on difficult topics from the Class 10 Maths syllabus instead of skipping them to avoid losing marks.

• Revise Formulas Daily:

Regular revision of  PW Class 10 Maths MIQs helps avoid calculation mistakes in exams.

• Practise Regularly:

Solve all CBSE Class 10  NCERT questions multiple times to strengthen your basics and improve accuracy.

• Solve Previous Year Papers:

Practising  CBSE Class 10 Previous Year Question Papers (PYQs) helps you understand question patterns and important topics.