Question

PLEASE HELP

Answer 1

Correct Answer: Option A

The next step in simplification will be to convert the squared term so that it no longer contains a square.

So, we are to simplify the term $cos^{2}(2x)$

Using the half-angle identity we can write:

$cos^{2}(2x)= \frac{1+cos(4x)}{2}$

Using this value, the equation becomes:

$sin^{4}x=1-2cos(2x)+ \frac{ \frac{1+cos(4x)}{2} }{4}$

Therefore, option A is the correct answer.