Question

If ${{\cos }^{-1}}\left( \frac{5}{13} \right)-{{\sin }^{-1}}\left( \frac{12}{13} \right)={{\cos }^{-1}}x,$ then $x$ is equal to

• A. $1$
• B. $\frac{1}{\sqrt{2}}$
• C. $0$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

Answer: (A)

$1$

Answer 2

Given, ${{\cos }^{-1}}\left( \frac{5}{13} \right)-{{\sin }^{-1}}\left( \frac{12}{13} \right)={{\cos }^{-1}}x$
$\Rightarrow$ ${{\sin }^{-1}}\left( \frac{12}{13} \right)-{{\sin }^{-1}}\left( \frac{12}{13} \right)={{\cos }^{-1}}x$
$\Rightarrow$ ${{\cos }^{-1}}x=0\Rightarrow \cos 0$
$\Rightarrow$ $x=1$