Question

Integral from -L to L cos(mPix/L)*cos(nPix/L)? (m, n are integers)?

Answer 1

\[\cos(a)\cos(b)=\frac{1}{2}[\cos(a+b)+\cos(a-b)]\]

Answer 2

\[\cos(\frac{ m \pi x }{L})\cos(\frac{npix}{L})=\frac{1}{2}\cos((\frac{m+n}{L})x)+\frac{1}{2}\cos((\frac{m-n}{L})x)\]