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in Sets, relations and functions by (54.5k points)

Prove that

tan-1(√(a(a + b + c)/bc)) + tan-1(√(b(a + b + c)/ac)) + tan-1(√(c(a + b + c)/bc)) = π, where a, b, c,> 0

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Best answer

Now, tan-1x + tan-1y + tan-1z

= tan-1((x + y + z - xyz)/(1 - xy - yz - zx)) = tan-1(0) = π

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