Question

If ${\cos }^{-1}x-{\sin }^{-1}x=0$, then $x$ is equal to-

• A. $\pm \frac{1}{\sqrt{2}}$
• B. $1$
• C. $\pm \frac{1}{\sqrt{3}}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is D $\frac{1}{\sqrt{2}}$

We know, ${\cos }^{-1}\theta +{\sin }^{-1}\theta =\frac{\pi }{2}$
$\therefore {\cos }^{-1}x-{\sin }^{-1}x=0$
$\Rightarrow {\cos }^{-1}x-\frac{\pi }{2}+{\cos }^{-1}x=0$
$\Rightarrow 2{\cos }^{-1}x=\frac{\pi }{2}\Rightarrow {\cos }^{-1}x=\frac{\pi }{4}$
$\Rightarrow x=\frac{1}{\sqrt{2}}$