Q. The value of $\cot^{- 1}{\frac{xy + 1}{x - y} + \cot^{- 1}{\frac{y\mathcal{z} + 1}{y - \mathcal{z}} + \cot^{- 1}\frac{\mathcal{z}x + 1}{\mathcal{z -}x}}}$ is
A) 0
B) 1
C) $\cot^{- 1}{x + \cot^{- 1}{y + \cot^{- 1}\mathcal{z}}}$
D) None of the above
Explanation
(a)
$\cot^{- 1}{\frac{xy + 1}{x - y} + \cot^{- 1}{\frac{y\mathcal{z} + 1}{y - \mathcal{z}} + \cot^{- 1}\frac{\mathcal{z}x + 1}{\mathcal{z -}x}}}$
$= \cot^{- 1}{y - \cos^{- 1}{x + \cot^{- 1}{\mathcal{z -}\cot^{- 1}{y + \cot^{- 1}{x - \cot^{- 1}\mathcal{z}}}}}}$
$= 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.