Answer
(a)$cos^{-1}(-x)=\pi-cos^{-1}x$
(b)$sec^{-1}(-x)=\pi-sec^{-1}x$
Work Step by Step
(a)Let
$cos^{-1}x=y$ ..................... eq (1)
$x=cosy$
$-x=-cosy$
$-x=cos(\pi-y)$
$cos^{-1}(-x)=\pi-y$ .................... eq (2)
Fom equation (1) and (2)
$cos^{-1}(-x)=\pi-cos^{-1}x$
(b)Let
$y=sec^{-1}x$ ...................... eq(3)
$secy=x$
$\frac{1}{cosy}=x$
$\frac{1}{x}=cosy$
$-\frac{1}{x}=-cosy$
$-\frac{1}{x}=cos(\pi-y)$
$\frac{1}{cos(\pi-y)}=-x$
$sec(\pi-y)=-x$
$\pi-y=sec^{-1}(-x)$ ....................... eq(4)
From equation (3) and equation (4)
$\pi-sec^{-1}x=sec^{-1}(-x)$
$sec^{-1}(-x)=\pi-sec^{-1}x$
