The value of ∆ = 1 sin ⁡ 3 θ sin 3 ⁡ θ 2 cos ⁡ θ sin ⁡ 6 θ sin 3 ⁡ 2 θ 4 cos 2 ⁡ θ - 1 sin ⁡ 9 θ sin 3 ⁡ 3 θ is equal to

Step-by-step solution

Multiplying C 1 by 3   s i n θ and dividing ∆ by 3   s i n θ , we get, ∆   = 1 3 sin ⁡ θ   3 sin ⁡ θ sin ⁡ 3 θ sin 3 ⁡ θ 3 sin ⁡ 2 θ sin ⁡ 6 θ sin 3 ⁡ 2 θ 3 sin ⁡ 3 θ sin ⁡ 9 θ sin 3 ⁡ 3 θ ∵ 3 sin ⁡ θ   4 cos 2 ⁡ θ - 1 = 3 sin ⁡ θ 3 - 4 sin 2 ⁡ θ = 3   sin ⁡ θ - 4 sin 3 ⁡ θ = 3 sin &#8