Looking for accurate SEBA Class 10 Maths Exercise 8.2 (Introduction to Trigonometry) textual solutions for the 2026–27 academic year? Access complete step-by-step solutions covering specific angle values (0°, 30°, 45°, 60°, 90°), evaluating trigonometric expressions, verifying identities, and solving for unknown angles (A and B) to score top marks in your HSLC board exams.
EXERCISE 8.2
1. Evaluate the following:
(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°)
(iv) (sin 30° + tan 45° – cosec 60°) / (sec 30° + cos 60° + cot 45°)
(v) (5 cos^2 60° + 4 sec^2 30° – tan^2 45°) / (sin^2 30° + cos^2 30°)
(vi) (cosec 30° + cosec 60° + cosec 90°) / (sec 0° + sec 30° + sec 60°)
(vii) (4 sin 30° + cos^2 45° – 4 cos^2 60°) / (2 sin 30° cos 30° + tan^2 45°)
2. Choose the correct option and justify your choice:
(i) (2 tan 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 2A = 2 sin A is true when A =
(A) 0°
(B) 30°
(C) 45°
(D) 60°
(iv) (2 tan 30°) / (1 – tan^2 30°) =
(A) cos 60°
(B) sin 60°
(C) tan 60°
(D) sin 30°
SEBA Class 10 Maths Exercise 8.2 Solutions
3. (i) If tan (A + B) = sqrt(3) and tan (A – B) = 1 / sqrt(3); 0° < A + B <= 90°; A > B, find A and B.
(ii) If sin (x + y) = 1, cos (x – y) = sqrt(3) / 2 and x > y, 0° <= x + y <= 90° then find x and y.
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 theta increases as theta increases.
(iii) The value of cos theta increases as theta increases.
(iv) sin theta = cos theta for all values of theta.
(v) cot A is not defined for A = 0°.
Class 10 Maths Chapter 8 Exercise 8.2 Question Answer SEBA 2026-27
5. Solve for theta, when 0° < theta < 90°:
(i) 2 cos^2 theta = 1
(ii) 3 tan^2 theta – 1 = 0
(iii) 2 cos 3theta = 1
(iv) sin theta – cos theta = 0
6. If tan theta = 1 / sqrt(3), then angle theta is: (a) 60° (b) 30° (c) 45° (d) 90°
Trigonometric Values Table Class 10 SEBA Ex 8.2 Solutions
7. In the following question a statement of assertion (A) is followed by a statement of reason (R). Assertion (A): The value of sin 45° is equal to cos 45°. Reason
(R): Value of cos theta is always equal to sin theta, when 0° < theta < 90°. Choose the correct option from the given alternative:
(a) Both assertion (A) and reason (R) are true and reason (R) is correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not correct explanation of assertion (A).
(c) Assertion (A) is true, but reason (R) is false.
(d) Assertion (A) is false, but reason (R) is true.
SEBA Class 10 Maths Chapter 8 Exercise 8.2 Textbook Answers
8. Which is the correct order of decreasing value of trigonometric ratios at 60°?
(a) sin 60° > cos 60° > tan 60°
(b) tan 60° > sin 60° > cos 60°
(c) tan 60° > cos 60° > sin 60°
(d) sin 60° > tan 60° > cos 60°
Class 10 Maths Exercise 8.2 Evaluate Trigonometric Ratios
📐 Updated Solutions Notice: This page features complete, step-by-step SEBA Class 10 Mathematics Chapter 8 (Introduction to Trigonometry) Exercise 8.2 Textual Solutions updated for the 2026–27 academic session. All standard angle value substitutions ($\sin 30^\circ$, $\cos 45^\circ$, $\tan 60^\circ$), expression evaluations, and angle-finding calculations strictly follow the latest revised Assam Board (SEBA/ASSEB) curriculum.
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