Answer
$L(x)=x$
Work Step by Step
$f(x)=\sin^{-1}x$,
$L(x)=f(a)+f'(a)(x-a)$
$f'(x)=\frac{1}{\sqrt{(1-x^2)}}$
$x_{0}=0$
$f(0)={\sin^{-1}0}=0$
$f'(0)= \frac{1}{1} = 1$
then $L(x)=0+1(x-0)=x$
$L(x)=x$
Thus, the final answer is: $L(x)=x$