Orthogonality relation for cosine on (0,pi)

Theorem

The following formula holds for $m,n \in \{0,1,2,\ldots\}$ with $m\neq n$: $$\displaystyle\int_0^{\pi} \cos(mt)\cos(nt) \mathrm{d}t=0,$$ where $\cos$ denotes cosine.

References

• 1978: T.S. Chihara: An Introduction to Orthogonal Polynomials ... (previous) ... (next) $(1.2)$