Class 10 Maths Chapter 9 Introduction to Trigonometry Exercise 9.3 NCERT Solutions
NCERT Solutions for class 10 Maths Chapter 9 Exercise 9.3 focuses on the application of trigonometric identities in solving problems. Instead of only verifying identities, this exercise requires you to use them to simplify expressions and evaluate values in a systematic way, which is part of the CBSE Class 10th syllabus..
These NCERT Solutions are presented step by step so that you can understand how to choose the correct identity and apply it at the right stage. With regular practise, this helps improve both clarity and accuracy in handling trigonometric expressions.
NCERT Solutions for Class 10 Maths Chapter 9 Exercise 9.3
1. Evaluate the following :
Answer:
(i) sin 60° cos 30° + sin 30° cos 60
(ii) 2 tan 2 45° + cos 2 30° – sin 2 60°
(iii) cos 45°/(sec 30° + cosec 30°)
(v) (5cos 2 60° + 4sec 2 30° - tan 2 45°)/(sin 2 30° + cos 2 30°
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°Answer:
(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°
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.
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.ion.
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:
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Build Strong Concepts:
Focus on understanding concepts in Class 10 Maths instead of memorising steps, as this helps in solving application-based questions.
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Work on Weak Areas:
Focus on difficult topics from the Class 10 Maths syllabus instead of skipping them to avoid losing marks.
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Revise Formulas Daily:
Regular revision of PW Class 10 Maths MIQs helps avoid calculation mistakes in exams.
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Practise Regularly:
Solve all CBSE Class 10 NCERT questions multiple times to strengthen your basics and improve accuracy.
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Solve Previous Year Papers:
Practising CBSE Class 10 Previous Year Question Papers (PYQs) helps you understand question patterns and important topics.
NCERT Solutions for Class 10 Maths Chapter 9 Exercise 9.3 FAQs
What if the angle is not given in the problem?
How do I approach a height and distance problem involving a right-angled triangle?
How do I handle multi-step problems in Exercise 9.3?
Is Exercise 9.3 important for the Class 10 board exam?
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