Finding ∫cos^2 x Using cos x cos y = 1/2(cos(x+y)+cos(x-y))

[jackscholar]

Homework Statement

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.

Homework Equations

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

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.

 

[eumyang]

Homework Statement

I need to find ∫cos^2x using cosxcosy=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.

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

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 cosxcosy=1/2(cos(x+y)+cos(x-y)) to cos2x so I can then use a general formula/rule. Any help is highly appreciated.

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
$\cos x \cos y = ... = \frac{1 + \cos 2x}{2}$.

 

[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?

 

[eumyang]

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?

Yes.