- #1

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- 49

## Homework Statement

Using the trig product identity, [itex]cosαcosβ=\frac{1}{2}[cos(α+β)+cos(α-β)][/itex], show that the time-average power at the detector can be written as P

_{avg}= 1+cos(δ)

That = is supposed to be a proportional symbol.

## Homework Equations

Other than the ones given in the problem statement, there are a few:

E

_{1}=E

_{0}cos(wt)

E

_{2}=E

_{0}cos(wt+δ)

[tex]δ=\frac{2∏(2x)}{λ}[/tex]

E

_{tot}=E

_{1}+E

_{2}

P = E

_{tot}

^{2}

That last = is supposed to be a proportional symbol.

## The Attempt at a Solution

Well, I started off by trying to square E

_{tot}, which gives me a long expression:

E

_{0}

^{2}cos

^{2}(wt)+E

_{0}

^{2}[cos(2wt+δ)+cos(δ)]+E

_{0}

^{2}cos

^{2}(wt+δ)

I'm not sure I did that right. I used the trig product rule.

From here, I can factor out an E

_{0}

^{2}, but I still have a bunch of cosine terms that I don't know what to do with. How in the world could I turn those into 1+cos(δ)?

Thanks.