Orthogonality relation for cosine on (0,pi)

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Theorem

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

Proof

References

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

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