Question

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

• A. 0.0
• B. 1
• C. $-1$
• D. 2

Answer 1

The correct option is B 1

We have
${\cos }^{-1}\frac{3}{5}-{\sin }^{-1}\frac{4}{5}={\cos }^{-1}x$
$\Rightarrow {\sin }^{-1}\left[\sqrt{1-\frac{a}{25}}\right]-{\sin }^{-1}\frac{4}{5}={\cos }^{-1}x$
$\Rightarrow {\sin }^{-1}\frac{4}{5}-{\sin }^{-1}\frac{4}{5}={\cos }^{-1}x$
$\Rightarrow {\cos }^{-1}x=0\Rightarrow x=\cos 0=1$
$\therefore x=1$