Question

The value of ${\mathrm{cosec}}^2\left({\cot }^{-1}x\right)-{\cot }^2\left({\mathrm{cosec}}^{-1}x\right)$ is equal to

• A. 5
• B. 2
• C. 3
• D. 1

Answer 1

Answer: (B)

${\mathrm{cosec}}^2\left({\cot }^{-1}x\right)-{\cot }^2\left({\mathrm{cosec}}^{-1}x\right)$
$=1+{\cot }^2\left({\cot }^{-1}x\right)-\left({\mathrm{cosec}}^2\left({\mathrm{cosec}}^{-1}x\right)-1\right)$
$=1+x^2-\left(x^2-1\right)=2$