First slide

Properties of ITF

Question

${cosec}^{- 1} (\cos x)$ is defined if

Moderate

A

$x \in [- 1, 1]$
B

$x \in R$
C

$x = (2 n + 1) \frac{π}{2}, n \in Z$
D

$x = n π, n \in Z$

Solution

We know that ${cosec}^{- 1} x$ is defined for
$x \in (- \infty, - 1] \cup [1, \infty)$ . Therefore, ${cosec}^{- 1} (\cos x)$ is defined for
$\cos x = \pm 1 \Rightarrow x = n π, n \in Z$ .

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