If $\sec^{- 1}{\sqrt{1 + x^{2}} + cosec^{- 1}\frac{\sqrt{1 + y^{2}}}{y} + \cot^{- 1}{\frac{1}{z} = \pi}}$, then $x + y + z$ is equal to

Question

Dr. Abubacker · Accepted Answer

(a)
Given, $sec^{- 1}\sqrt{1 + x^{2}} + cosec^{- 1}\frac{\sqrt{1 + y^{2}}}{y} + \cot^{- 1}{\frac{1}{z} = \pi}$
$	herefore\ 	an^{- 1}{x + 	an^{- 1}{y + 	an^{- 1}{z = \pi}}}$
$\Rightarrow \ \ \ 	an^{- 1}{\left( \frac{x + y + z - xyz}{1 - xy - yz - zx} ight) = \pi}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x + y + z = xyz$

Q. If $\sec^{- 1}{\sqrt{1 + x^{2}} + cosec^{- 1}\frac{\sqrt{1 + y^{2}}}{y} + \cot^{- 1}{\frac{1}{z} = \pi}}$, then $x + y + z$ is equal to

Explanation

Reviewed by Dr. Abubacker

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