# Proving identities

• Dec 31st 2008, 11:46 PM
ImKo
Proving identities
Prove that

cos theta / 2 = sqrt[1 + (cos theta / 2)]

I know this is somewhat similar to cosine - half of an angle identity or formula

But I'm having trouble with the division bar, it only divides cos theta not the whole 1 + cos theta. As a result, I can't prove it

Is (1 + cos theta ) / 2 the same to 1 + cos theta /2 ?

• Jan 1st 2009, 12:15 AM
kalagota
Quote:

Originally Posted by ImKo
Prove that

cos theta / 2 = sqrt[1 + (cos theta / 2)]

I know this is somewhat similar to cosine - half of an angle identity or formula

But I'm having trouble with the division bar, it only divides cos theta not the whole 1 + cos theta. As a result, I can't prove it

Quote:

Originally Posted by ImKo
Is (1 + cos theta ) / 2 the same to 1 + cos theta /2 ?

$\cos \left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{1+\cos\theta}{2}}$
if this is the case, use the indentity $\cos 2\alpha = 2\cos^2 (\alpha) - 1$ and let $\alpha=\dfrac{\theta}{2}$