Answer
(a)$sin^{-1}(-x)=-sin^{-1}x$
(b) $tan^{-1}(-x)=-tan^{-1}x$
Work Step by Step
(a)Let
$\sin^{-1}(-x)=y$ ................. eq (1)
$\Longrightarrow$ $-x=siny$ Or
$x=-siny=sin(-y)$
Now
$x=sin(-y)$ $ \Longrightarrow$ $sin^{-1}x=-y$ Or
$-sin^{-1}x=y$ .............. eq (2)
From equation (1) and equation (2)
$sin^{-1}(-x)=-sin^{-1}x$
(b)Let
$tan^{-1}(-x)=y$ ...................... eq (3)
$\Longrightarrow$
$tany=-x$ Or
$-tany=x$ Or
$tan(-y)=x$
$tan^{-1}x=-y$ Or
$-tan^{-1}x=y$ .................... eq (4)
From equation (3) and equation (4)
$tan^{-1}(-x)=-tan^{-1}x$
