Hello! Please help!! I really need this.

Lets show that:

cos x cos 2x cos 4x cos 8x = sin 16x / 16 sinx

Use formula:

sin 2x = 2 sin x cos x

Multiply LHS by 2sinx/2sinx:

2sinx cos x cos 2x cos 4x cos 8x / 2 sin x = sin 2x  cos 2x cos 4x cos 8x / 2 sin x = 2sin 2x cos 2x cos 4x cos 8x / 4 sin x =sin 4x  cos 4x cos 8x / 4 sin x =2sin 4x  cos 4x cos 8x / 8 sin x =sin 8x cos 8x / 8 sin x =2 sin 8x cos 8x / 16 sin x =sin 16x / 16 sin x

Now, we can easily find that:

sin (16*2π/15) = sin (2π/15)

Coming back to the original equation, we get:

cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = sin (16*2π/15) / 16 sin (2π/15) cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = 1/16