Is it true that $\int_{0}^{\infty}\sin(mx)\sin(nx) \, dx = \delta (m-n) $ although using Euler formula I get a linear combination of $ \delta(m-n) $ and $ \delta (m+n)$?
What is the sum $\sum_{n=0}^\infty (-1)^n \sin(nx)$?
Here $\delta (x)$ is the Dirac delta function.