Integrating sin(x) * sin(x+1) dx

I think we need to use integration by parts since this problem is under the integration by parts section.

Could someone please explain to me how to integrate this problem because, when I do it (using integration by parts), I get a meaningless tautology where sin(1) = some_constant!

Question

Integrating sin(x) * sin(x+1) dx


I think we need to use integration by parts since this problem is under the integration by parts section.

Could someone please explain to me how to integrate this problem because, when I do it (using integration by parts), I get a meaningless tautology where sin(1) = some_constant!

s3a · Answer

You don't need to do all the work; just telling me what to do, in a few words, would be good enough.

amistre64 · Answer

sin(a+b) = sina cosb + sinb cosa

might be useful ... but might not :)

s3a · Answer

Actually, I just found sin(a) sin(b) = 1/2 cos(a-b) - 1/2 cos(a+b), which worked well for me. Thanks, nonetheless! :)

amistre64 · Answer

thatll work fin too :)

s3a · Answer

Alright, thanks again. See you later.

anonymous · Answer

$$2\sin a \sin b=\cos \left( a-b \right)-\cos \left( a+b \right)$$