Question

If θ = 30°, verify that: sin 3θ = 4sinθ . sin(60° - θ) sin(60° + θ)

Answer 1

Given: θ = 30°
sin3θ
= sin3 x 30°
= sin90°
= 1
4sinθ . sin(60° - θ) sin(60° + θ)
= 4sin 30° x sin(60° - 30°) x sin(60° + 30°)
= 4sin30° x sin30° x sin90°

= `4 xx (1)/(2) xx (1)/(2) xx 1`
= 1
⇒ sin3θ = 4sinθ . sin(60° - θ)sin(60° + θ).