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

The Correct Option is A

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 $