# ? Each time you see (cos(2x))^2, replace it with 1/2 + 1/2cos(4x) ?

• Feb 27th 2009, 03:11 PM
estex198
? Each time you see (cos(2x))^2, replace it with 1/2 + 1/2cos(4x) ?
I understand sin(2x)^2 = 1/2 - 1/2cos(2x), due to the double number identity: cos2x = 1 - 2sin(x)^2.

***[My question is how does (cos(2x))^2 = 1/2 + 1/2cos(4x) ???]***

I've tried reworking the identity every which way and can't seem to find out how the two are equivalent. Thanks in advance!
• Feb 27th 2009, 03:17 PM
mr fantastic
Quote:

Originally Posted by estex198
I understand sin(2x)^2 = 1/2 - 1/2cos(2x), due to the double number identity: cos2x = 1 - 2sin(x)^2.

***[My question is how does (cos(2x))^2 = 1/2 + 1/2cos(4x) ???]***

I've tried reworking the identity every which way and can't seem to find out how the two are equivalent. Thanks in advance!

$\cos (2A) = \cos^2 A - \sin^2 A = 2 \cos^2 A - 1 \Rightarrow \cos^2 A = \frac{1}{2} (\cos (2A) + 1)$.
$A = 2x$ in your case.