Class 11th Maths – RD Sharma Chapter 8 : Trigonometric Formulae – Exercise 8.1 Solutions (Step-by-Step Guide)

1. Express each of the following as the sum or difference of sines and cosines: (i) 2 sin 3x cos x (ii) 2 cos 3x sin 2x (iii) 2 sin 4x sin 3x (iv) 2 cos 7 x cos 3x Watch Solution
2. Prove that: 2 sin 5π/12 sin π/12 = 1/2 Watch Solution
3. Prove that: 2 cos 5π/12 cos π/12 = 1/2 Watch Solution
4. Prove that: 2 sin (5π/12) cos (π/12) = (√3 + 2)/2 Watch Solution
5. Show that: sin 50° cos 85° = (1 − √2 sin 35°) / (2√2) Watch Solution
6. Show that: sin 25° cos 115° = 1/2(sin 140° – 1) Watch Solution
7. Prove that: 4 cos x cos (π/3 + x) cos(π/3 – x) = cos 3x Watch Solution
8. Prove that: cos 10° cos 30° cos 50° cos 70° = 3/16 Watch Solution
9. Prove that: cos 40° cos 80° cos 160° = – 1/8 Watch Solution
10. Prove that: sin 20° sin 40° sin 80° = √3/ 8 Watch Solution
11. Prove that: cos 20° cos 40° cos 80° = 1/8 Watch Solution
12. Prove that: tan 20° tan 40° tan 60° tan 80° = 3 Watch Solution
13. Prove that: tan 20° tan 30° tan 40° tan 80° = 1 Watch Solution
14. Prove that: sin 10° sin 50° sin 60° sin 70° = √3/16 Watch Solution
15. Prove that: sin 20° sin 40° sin 60° sin 80° = 3/16 Watch Solution
16. Show that: sin A sin (B – C) + sin B sin (C – A) + sin C sin (A – B) = 0 Watch Solution
17. Show that: sin (B – C) cos (A – D) + sin (C – A) cos (B – D) + sin (A – B) cos (C – D) = 0 Watch Solution
18. If α + β = π/2, show that the maximum value of cos α cos β is 1/2. Watch Solution
19. Prove that: tan x tan(π/3 − x) tan(π/3 + x) = tan 3x Watch Solution