Let a, b and c be positive real numbers. Then prove that `tan^(-1) sqrt((a(a + b + c))/(bc)) + tan^(-1) sqrt((b (a + b + c))/(ca)) + tan^(-1) sqrt((c(a + b+ c))/(ab)) =' pi'

Explanation

To prove that

\[ \tan^{-1} \sqrt{\frac{a(a + b + c)}{bc}} + \tan^{-1} \sqrt{\frac{b(a + b + c)}{ca}} + \tan^{-1} \sqrt{\frac{c(a + b + c)}{ab}} = \pi, \]

where \(a\), \(b\), and \(c\) are positive real numbers, we can follow these steps:

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