Question

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

• A. $\sqrt{1 + x^{2}}$
• B. $x$
• C. $\frac{1}{\sqrt{1 + x^{2}}}$
• D. $\sqrt{1 - x^{2}}$

Answer 1

Answer: (C)

Let, $\left(cot\right)^{- 1} \text{x} = \text{A} , \, (cot)^{2} A = x^{2}$
$1+(cot)^{2} A =1+x^{2}=cosec^{2}A$
$\frac{1}{\text{sin}^{2 \, } \text{A}} = 1 + \text{x}^{2} \, \, ⇒ \, \, \text{sin } \text{A} = 1 / \sqrt{1 + \text{x}^{2}}$
$\Rightarrow \text{sin} \left(\text{cot}^{-1 \, } \text{x}\right) = 1 / \sqrt{1 + \left(\text{x}\right)^{2}}$