Question

The value of $cos\left({\sin }^{-1}\frac{\pi }{3}+{\cos }^{-1}\frac{\pi }{3}\right)$ is

• A. 0
• B. 1
• C. -0
• D. Does not exist

Answer 1

Answer: (D)

$\pi /3\notin [-1,1]$ which is the domain of ${\sin }^{-1}x,{\cos }^{-1}x$
So, $\cos \left({\sin }^{-1}\pi /3+{\cos }^{-1}\pi /3\right)$ does not exist.