Prove that

To Prove:

Taking LHS,

= cosx cos2x cos4x cos8x

Multiply and divide by 2sinx, we get

[∵ sin 2x = 2 sinx cosx]

Multiply and divide by 2, we get

We know that,

sin 2x = 2 sinx cosx

Replacing x by 2x, we get

sin 2(2x) = 2 sin(2x) cos(2x)

or sin 4x = 2 sin 2x cos 2x

Multiply and divide by 2, we get

We know that,

sin 2x = 2 sinx cosx

Replacing x by 4x, we get

sin 2(4x) = 2 sin(4x) cos(4x)

or sin 8x = 2 sin 4x cos 4x

Multiply and divide by 2, we get

We know that,

sin 2x = 2 sinx cosx

Replacing x by 8x, we get

sin 2(8x) = 2 sin(8x) cos(8x)

or sin 16x = 2 sin 8x cos 8x

= RHS

∴ LHS = RHS

Hence Proved