Question

Taking θ = 30°, verify that : sin3θ = 3 sinθ – 4 sin³θ

Answer 1

To verify : sin3 = 3sin – 4 sin3 

Given that = 30° 

L.H.S = sin 3 = sin (3× 30°) = sin(90°) = 1. (∵ sin90° = 1) 

R.H.S = 3 sin – 4sin³ = 3sin30° – 4 sin³30°

3 x \(\frac{1}{2} - 4(\frac{1}{2})^3\)   (\(\because sin 30° = 1\))

\(\frac{3}{2} - \frac{4}{8} = \frac{3}{2} - \frac{1}{2} = \frac{2}{2} = 1.\)

Hence, L.H.S = R.H.S. 

Therefore, for =30°, sin3 = 3sin – 4sin³. 

Hence Proved