Question

Find the angle θ when 0° < θ < 90°.

sin 8 = 2 sin 30° cos 30°

Answer 1

Given:

sin 8 = 2 sin 30° cos 30°

Step 1:

sin 2A = 2sin A cos A

2sin 30° cos 30°

sin⁡ 2A with A = 30°

2 sin 30° cos 30° = sin(2 × 30°)

Step 2: 

sin (60°) = `sqrt3/2`

sin θ = sin 60°    ...[0° < θ < 90°]

θ = 60°