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If tan ((p pi)/4)=cot ((qpi)/4), then pr...

If `tan ((p pi)/4)=cot ((qpi)/4)`, then prove that `p+q=2(2n+1), n in Z`.

Text Solution

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`tan((p pi)/4)=cot ((qpi)/4)=tan (pi/2-(qpi)/4)`
`rArr (p pi)/4= n pi+pi/2-(q pi)/4`
or `p/4=n+1/2-q/4`
or `(p+q)/4=(2n+1)/2`
or `p+q=2(2n+1), n in Z`
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