Need explanation about sin rule

[MissP.25_5]

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

 

[.Scott]

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

 

[NascentOxygen]

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

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?

 

[D H]

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