Question

Find the value of $\cos ({\sec }^{-1}\mathrm{x}+{\mathrm{cosec}}^{-1}\mathrm{x}),\left|\mathrm{x}\right|\ge 1.$

• A. 1
• B. 0
• C. -1
• D. 2

Answer 1

The correct option is B

0

Explanation for the correct option

We know that,

${\sec }^{-1}\mathrm{x}+{\mathrm{cosec}}^{-1}\mathrm{x}=\frac{\mathrm{\pi }}{2}$

$\cos ({\sec }^{-1}\mathrm{x}+{\mathrm{cosec}}^{-1}\mathrm{x})=\cos \frac{\mathrm{\pi }}{2}$

$=0$

Hence option (B) is the correct answer.