# Integral of cos^2 x

1. Mar 22, 2013

### jackscholar

1. The problem statement, all variables and given/known data

I need to find ∫cos^2 x using cos x cos y = 1/2(cos(x+y)+cos(x-y)). Note that it is not cos to the power of 2x. It is cos to the power of 2 multiplied by x.

2. Relevant equations

cos x cos y = 1/2(cos(x+y)+cos(x-y))

3. The attempt at a solution

I've searched my textbook and online everywhere, but my teacher hasn't given me any guidance. All I can think of is somehow converting cos x cos y = 1/2(cos(x+y)+cos(x-y)) to cos2x so I can then use a general formula/rule. Any help is highly appreciated.

Last edited by a moderator: Mar 22, 2013
2. Mar 22, 2013

### eumyang

Minor nitpick, but one does not say "multiplied" here. You read it as "cosine squared of x."

If you are saying that
$\cos x \cos y = ... = \cos 2x$,
after you plug in x for y, that's not right. It should be
$\cos x \cos y = ... = \frac{1 + \cos 2x}{2}$.

3. Mar 22, 2013

### jackscholar

By, after you plug in x for y, do you mean to say that you change cosxcosy to cosxcosx in order to satisfy cosine squared of x?

4. Mar 22, 2013

Yes.