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Evaluate : intcosmxcosnxdx,"when (i) "m!...

Evaluate : `intcosmxcosnxdx,"when (i) "m!=n` (ii) m=n.

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(i) When `m!=n`, we have
`intcosmxcosnxdx=(1)/(2)int[cos(m+n)x+cos(m-n)x]dx`
`=(1)/(2)intcos(m+n)xdx+(1)/(2)intcos(m-n)xdx`
`=(sin(m+n)x)/(2(m+n))+(sin(m-n)x)/(2(m-n))+C`.
(ii) When m=n. we have
`intcosmxcosnxdx=intcos^(2)nxdx`
`(1)/(2)int2cos^(2)nxdx=(1)/(2)int(1+cos2nx)dx`
`(1)/(2)intdx+(1)/(2)intcos2nxdx=(x)/(2)+(sin2nx)/(4n)+C`.
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