Question
Show that for all integers $m$ and $n,$ with $m \neq \pm n$ $\int_{-x}^{\pi} \sin m \theta \sin n \theta d \theta=0.$
Show that for all integers $m$ and $n,$ with $m \neq \pm n$ $\int_{-x}^{\pi} \sin m \theta \sin n \theta d \theta=0.$
Answers
Prove the formula, where $ m $ and $ n $ are positive integers.
$ \displaystyle \int_{-\pi}^{\pi} \sin mx \cos nx dx = 0 $
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