# Simplify expression by eliminating radical

• August 29th 2010, 06:30 PM
yzobel
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!
• August 29th 2010, 06:49 PM
pickslides
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?
• August 29th 2010, 06:54 PM
yzobel