Chapter 7.3, Problem 57ES

Evaluate the integral.

Let m, n be distinct nonnegative integers. Use formulas (16)-(18) to prove :

$\begin{array}{l}\left(\text{a}\right){\displaystyle {\int }_0^{2\pi }\sin mx\cos nxdx=0}\\ \left(\text{b}\right){\displaystyle {\int }_0^{2\pi }\cos mx\cos nxdx=0}\\ \left(\text{c}\right){\displaystyle {\int }_0^{2\pi }\sin mx\sin nxdx=0}.\end{array}$