Please help me simplify the following trig expression?

Question

Simplify sin(x)cos(x)cos(2x) .

This is my attempt:

sin(x)cos(x)[cos^2(x) - sin^2(x)]

sin(x)cos^3(x) - sin^3(x)cos(x)

Then I'm stuck because of the power of 3..

Any help is appreciated. Much thanks.

Answer 1

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

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

(1/2)sin(2x)cos(2x)

(1/4) sin (4x)   seems to be the result.

.