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Ifp > q > 0a n dp r < -1 < q r , then fi...

If`p > q > 0a n dp r < -1 < q r ,` then find the value of `tan^(-1)((p-q)/(1+p q))+tan^(-1)((q-r)/(1+q r))+tan^(-1)((r-p)/(1+r p))`.

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To solve the problem, we need to evaluate the expression: \[ \tan^{-1}\left(\frac{p-q}{1+pq}\right) + \tan^{-1}\left(\frac{q-r}{1+qr}\right) + \tan^{-1}\left(\frac{r-p}{1+rp}\right) \] Given the conditions \( p > q > 0 \) and \( pr < -1 < qr \), we will analyze each term step by step. ...
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