Question

If ${\cos }^{-1}\frac{3}{5}-{\sin }^{-1}\frac{4}{5}={\cos }^{-1}x$, then $x$ is equal to-

• A. $0$
• B. $1$
• C. $-1$
• D. none of these

Answer 1

The correct option is B $1$

Given, ${\cos }^{-1}\frac{3}{5}-{\sin }^{-1}\frac{4}{5}={\cos }^{-1}x$
$\Rightarrow {\cos }^{-1}\frac{3}{5}-{\cos }^{-1}\left(\sqrt{1-{\left(\frac{4}{5}\right)}^2}\right)={\cos }^{-1}x$
$\Rightarrow {\cos }^{-1}\frac{3}{5}-{\cos }^{-1}\frac{3}{5}={\cos }^{-1}x$
$\Rightarrow 0={\cos }^{-1}x$

$\Rightarrow x=1$