# Lowering Powers - Simplify in terms of cosine

• Nov 12th 2009, 03:03 PM
l flipboi l
Lowering Powers - Simplify in terms of cosine
Hello,

Can someone please show me all the algebraic steps for simplifying cos^4x?

The problem should be

cos^4x = ((1+cos2x)/2)((1+cos2x)/2)

thanks!
• Nov 12th 2009, 03:38 PM
pickslides
$\displaystyle \cos^4(x) = (\cos^2(x))^2 = \left(\frac{1+\cos(x)}{2}\right)^2 = \left(\frac{1+\cos(x)}{2}\right) \times \left(\frac{1+\cos(x)}{2}\right)$

Have a look at this.

Table of Trigonometric Identities
• Nov 12th 2009, 04:29 PM
l flipboi l
Quote:

Originally Posted by pickslides
$\displaystyle \cos^4(x) = (\cos^2(x))^2 = \left(\frac{1+\cos(x)}{2}\right)^2 = \left(\frac{1+\cos(x)}{2}\right) \times \left(\frac{1+\cos(x)}{2}\right)$

Have a look at this.

Table of Trigonometric Identities

Thanks!

Although i'm stuck at this part, 1/4(cos^4x+2cos^2x+1)

what else could I do?
• Nov 12th 2009, 04:33 PM
pickslides
You are expanding something that does not need to be expanded. You will only end up back at the start.