First slide

Properties of ITF

Question

Range of $\sin^{- 1} x - \cos^{- 1} x$ is

Easy

A

$[\frac{- 3 π}{2}, \frac{π}{2}]$
B

$[\frac{- 5 π}{3}, \frac{π}{3}]$
C

$[\frac{- 3 π}{2}, π]$
D

$[0, π]$

Solution

Let $y = \sin^{- 1} x - \cos^{- 1} x = \frac{π}{2} - 2 \cos^{- 1} x$
$S in c e 0 \leq \cos^{- 1} x \leq π \Rightarrow - 2 π \leq - 2 \cos^{- 1} x \leq 0 \Rightarrow \frac{π}{2} - 2 π \leq \frac{π}{2} - 2 \cos^{- 1} x \leq 0 \Rightarrow - \frac{3 π}{2} \leq y \leq \frac{π}{2}$

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