Simplify expression by eliminating radical

**yzobel** · August 29th 2010, 05:30 PM

How can I simplify this expression:

f(theta)= sqrt(1+cos(4theta))

by eliminating the radical? Is there a specific idenity I have to use?

Thank you, I appreciate any help!

**pickslides** · August 29th 2010, 05:49 PM

Maybe this can help

$\displaystyle \cos^2u = \frac{1+\cos(2u)}{2}$

$\displaystyle \cos u = \sqrt{\frac{1+\cos(2u)}{2}}$

$\displaystyle \sqrt{2}\cos u = \sqrt{1+\cos(2u)}$

Therefore

$\displaystyle \sqrt{2}\cos 2\theta = \sqrt{1+\cos(4\theta)}$

You still have $\displaystyle \sqrt{2}$ in the desired expression. Is this helpful at all?

**yzobel** · August 29th 2010, 05:54 PM

Very helpful. Thank you!

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