Rewrite in terms of the first power

Question

Sin²6x cos²6x

Answer 1

Since sin(2a) = 2 sin(a)cos(a)

Then sin²(2a) = 4sin²(a)cos²(a)

or (1/4)sin²(2a) = sin²(a)cos²(a)

Using the identity sin²(a) = (1/2) - (1/2)cos(2a)

(1/4)sin²(2a) = (1/8) - (1/8)cos(4a) if a = 6x

Then

(1/4)sin²(12x) = (1/8) - (1/8)cos(24x) = sin²(6x)cos²(6x)