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Question: The value of \(\sin \left( \cot ^ { - 1 } x \right)\) is...

The value of sin⁡(cot⁡−1x)\sin \left( \cot ^ { - 1 } x \right) is

A

(1+x2)3/2\left( 1 + x ^ { 2 } \right) ^ { 3 / 2 }

B

(1+x2)−3/2\left( 1 + x ^ { 2 } \right) ^ { - 3 / 2 }

C

(1+x2)1/2\left( 1 + x ^ { 2 } \right) ^ { 1 / 2 }

D

(1+x2)−1/2\left( 1 + x ^ { 2 } \right) ^ { - 1 / 2 }

Answer

(1+x2)−1/2\left( 1 + x ^ { 2 } \right) ^ { - 1 / 2 }

Explanation

Solution

sin⁡(cot⁡−1x)\sin \left( \cot ^ { - 1 } x \right) = sin⁡(sin⁡−111+x2)\sin \left( \sin ^ { - 1 } \frac { 1 } { \sqrt { 1 + x ^ { 2 } } } \right) = 11+x2\frac { 1 } { \sqrt { 1 + x ^ { 2 } } }