Question

PLEASE HELP
Look at the proof showing sin^4x=3-4cos2x+cos4x/8. Which expression will complete the fourth step of the proof?
sin^4x=(sin^2x)^2
sin^4x=(1-cos2x/2)^2
sin^4x=1-2cos2x+cos^22x/4
sin^4x=?
A.) 1-2cos2x+(1+cos4x/2)/4
B.)1-2cos2x+1+cos4x/4
C.)1-2cos2x+(1+cos2x/2)/4
D.)1-2cos2x+1-cos2x/4

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.