# Thread: Lowering Powers - Simplify in terms of cosine

1. ## 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!

2. $\displaystyle \cos^4(x) = (\cos^2(x))^2 = \left(\frac{1+\cos(x)}{2}\right)^2 = \left(\frac{1+\cos(x)}{2}\right) \times \left(\frac{1+\cos(x)}{2}\right)$

Have a look at this.

Table of Trigonometric Identities

3. 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?

4. You are expanding something that does not need to be expanded. You will only end up back at the start.

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### cos^4x) power reducing

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