Solveeit Logo
Login

Question

Question: \(\cot ^ { - 1 } \frac { x y + 1 } { x - y } + \cot ^ { - 1 } \frac { y z + 1 } { y - z } + \cot ^ {...

cot⁡−1xy+1x−y+cot⁡−1yz+1y−z+cot⁡−1zx+1z−x=\cot ^ { - 1 } \frac { x y + 1 } { x - y } + \cot ^ { - 1 } \frac { y z + 1 } { y - z } + \cot ^ { - 1 } \frac { z x + 1 } { z - x } =

A

0

B

1

C

cot⁡−1x+cot⁡−1y+cot⁡−1z\cot ^ { - 1 } x + \cot ^ { - 1 } y + \cot ^ { - 1 } z

D

None of these

Answer

0

Explanation

Solution

cot⁡−1xy+1x−y+cot⁡−1yz+1y−z+cot⁡−1zx+1z−x\cot ^ { - 1 } \frac { x y + 1 } { x - y } + \cot ^ { - 1 } \frac { y z + 1 } { y - z } + \cot ^ { - 1 } \frac { z x + 1 } { z - x }

=cot⁡−1y−cot⁡−1x+cot⁡−1z−cot⁡−1y= \cot ^ { - 1 } y - \cot ^ { - 1 } x + \cot ^ { - 1 } z - \cot ^ { - 1 } y +cot⁡−1x−cot⁡−1z=0+ \cot ^ { - 1 } x - \cot ^ { - 1 } z = 0.

Note: Students should remember this question as a formula.