16 sin 20 ° sin 40 ° sin 80 ° is equal to

Step-by-step solution

We know that sin θ sin 60 - θ sin 60 + θ = 1 4 sin 3 θ Now given 16 sin 20 ° sin 40 ° sin 80 ° Comparing with above formula θ = 20 ° we get 16 sin 20 ° sin 40 ° sin 80 ° = 16 × 1 4 × sin 3 × 20 ° = 16 × 1 4 × sin 60 ° = 4 × 3 2 = 2 3