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

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