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Question

Mathematics Question on Properties of Inverse Trigonometric Functions

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

A

1+x2\sqrt{1+x^2}

B

xx

C

(1+x2)−3/2(1+x^2)^{-3/2}

D

(1+x2)−1/2(1+x^2)^{-1/2}

Answer

(1+x2)−1/2(1+x^2)^{-1/2}

Explanation

Solution

Put cot−1x=Acot^{-1} x=A ∴x=cot A\therefore x=cot\,A ∴sin A=1x2+1=(1+x2)−1/2 \therefore sin\,A = \frac{1}{\sqrt{x^{2}+1}} = \left(1+x^{2}\right)^{-{1}/{2}}