If , , and are positive, show that ^ -1 a(a+b+c) bc + ^ -1 b(a+b+c) ac + ^ -1…

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If aa, bb, and cc are positive, show that tan⁡−1a(a+b+c)bc+tan⁡−1b(a+b+c)ac+tan⁡−1c(a+b+c)ab=π.\tan^{-1}\sqrt{\frac{a(a+b+c)}{bc}}+\tan^{-1}\sqrt{\frac{b(a+b+c)}{ac}}+\tan^{-1}\sqrt{\frac{c(a+b+c)}{ab}}=\pi.

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