# Need explanation about sin rule

1. Jan 27, 2014

### MissP.25_5

Hello.
This is part of a solution but I don't understand the underlined part. Why is it equals to 0?

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2. Jan 27, 2014

### .Scott

sin(wt)/6 x sin(2wt-(pi/4))
is not equal to zero.

3. Jan 29, 2014

### Staff: Mentor

That term itself isn't zero. But the area under it, taken over the complete cycle 0→2 Pi contributes nothing to the integral that you are about to evaluate. So the author is just looking ahead and seeing that he can save himself a bit of work here, and not bothering to process a term that is going to end up as zero anyway.

Why don't you work through without dismissing that term, and see how the result pans out?

4. Jan 29, 2014

### D H

Staff Emeritus
An easy way to show that that term integrates to zero is to use the identity $\sin(a)\sin(b) = \frac 1 2 \bigl(\cos(a-b) - \cos(a+b)\bigr)$.

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