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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`.

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To solve the equation \( \tan\left(\frac{p \pi}{4}\right) = \cot\left(\frac{q \pi}{4}\right) \), we can start by using the identity that relates tangent and cotangent. ### Step 1: Rewrite cotangent in terms of tangent We know that: \[ \cot(x) = \frac{1}{\tan(x)} \] Thus, we can rewrite the equation as: ...
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