Value of Trigonometric Functions at Multiples and Submultiples of an angle – Exercise 9.2 Solutions

1. Prove that: sin 5x = 5 sin x – 20 sin³ x + 16 sin⁵ x  Watch Solution
2. Prove that: 4 (cos³ 10° + sin³ 20°) = 3 (cos 10° + sin 20°) Watch Solution
3. Prove that: cos³ x sin 3x + sin³ x cos 3x = 3/4 sin 4x Watch Solution
4. Prove that: tan x tan (x + π/3) + tan x tan (x – π/3) + tan (x + π/3) tan (x – π/3) = – 3 Watch Solution
5. Prove that: tan x + tan (π/3 + x) – tan (π/3 – x) = 3 tan 3x Watch Solution
6. Prove that: cot x + cot (π/3 + x) – cot (π/3 – x) = 3 cot 3x Watch Solution
7. Prove that: cot x + cot (π/3 + x) + cot (2π/3 + x) = 3 cot 3x Watch Solution
8. Prove that: sin 5x = 5 cos⁴ x sin x – 10 cos² x sin³ x + sin⁵ x Watch Solution
9. Prove that: sin³ x + sin³ (2π/3 + x) + sin³ (4π/3 + x) = –3/4 sin 3x. Watch Solution
10. Prove that: |sin x sin (π/3 – x) sin (π/3 + x)| ≤ 1/4 for all values of x. Watch Solution
11. Prove that: |cos x cos (π/3 – x) cos (π/3 + x)| ≤ 1/4 for all values of x. Watch Solution