Question

$\sec \left( \operatorname { cosec } ^ { - 1 } x \right)$ is equal to.

• A. $\operatorname { cosec } \left( \sec ^ { - 1 } x \right)$
• B. $\cot x$
• C. $\pi$
• D. None of these

Answer 1

Answer: (A)

$\operatorname { cosec } \left( \sec ^ { - 1 } x \right)$

Answer 2

We know that

sec(cosec^–1x) = cosec(sec^–1 x)

$= \frac { | x | } { \sqrt { x ^ { 2 } - 1 } }$, for $| x | > 1$.