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Question: If xy + yz + zx =1, than tan<sup>–1</sup> x + tan<sup>–1</sup> y + tan<sup>–1</sup> z is equal to –...

If xy + yz + zx =1, than tan–1 x + tan–1 y + tan–1 z is equal to –

A

p

B

p/2

C

0

D

None of these

Answer

None of these

Explanation

Solution

tan–1x + tan–1y + tan–1z

= tan–1 (x+y+z−xyz1−xy−yz−zx)\left( \frac { x + y + z - x y z } { 1 - x y - y z - z x } \right) = π2\frac { \pi } { 2 }

but will not lie in the domain of tan–1 x. so, none of these is appropriate answer.