First slide

Properties of ITF

Question

$C o s e e^{- 1} (C o s x)$ is defined if

Moderate

A

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

$x \in R$
C

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

$x = n π, n \in I$

Solution

$C o s e e^{- 1} (C o s x)$ $i s d e f i n e d o n l y i f$ $C o s x \in (- \infty, - 1] \cup [1, \infty)$
$\Rightarrow \cos x = \pm 1 (∵ (- 1 \leq \cos x \leq 1)) \Rightarrow x = n π, n \in I$

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