Question

$\underset{x\to 0^{-}}{lim}\left\{{\sin }^{-1}\right[\tan x\left]\right\}=l$ then $l$ is equal to
where $\left[\right]$ and $\left\{\right\}$ denotes greatest the integer and fraction part function

• A. $0$
• B. $-{\sin }^{-1}\left(1\right)$
• C. $\sin 1$
• D. $2-\frac{\pi }{2}$

Answer 1

The correct option is D $2-\frac{\pi }{2}$

$\underset{x\to 0^{-}}{lim}\left\{{\sin }^{-1}\right[\tan x\left]\right\}$
$=\underset{x\to 0^{-}}{lim}\left\{{\sin }^{-1}\right[0^{-}\left]\right\}$
$=\underset{x\to 0^{-}}{lim}\left\{{\sin }^{-1}\right(-1\left)\right\}$

$=-\pi /2$
$=2-\pi /2$