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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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Knowledge Check

  • If p=tan(-(11pi)/(6)),q=tan((21pi)/(4))and r = cot ((283pi)/(6)) , then which of the following is / are correct ? 1. The value of pxxr is 2. 2. p , q and r are in G . P . Select the correct anwer using the code given below :

    A
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    B
    2 only
    C
    Both 1 and 2
    D
    Neither 1 nor 2

  • If p= tan(-(11pi)/(6)).q=tan((21pi)/(4)) and r=cot ((383pi)/(6)) , then which of the following is/are correct? 1.The value of pxxr is 2 2.p.q and r are in G.P Select the correct answer using the code given below:

    A
    Only 1
    B
    Only 2
    C
    Both 1 and 2
    D
    Neither 1 nor 2

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