Question

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

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

Answer 1

The Correct Option is D

We need to find the value of \(\cos(\sin^{-1}(\frac{\pi}{3}) + \cos^{-1}(\frac{\pi}{3}))\).

First, note that the domain of both \(\sin^{-1}(x)\) and \(\cos^{-1}(x)\) is \([-1, 1]\). However, \(\frac{\pi}{3} \approx \frac{3.14}{3} > 1\). Therefore, \(\sin^{-1}(\frac{\pi}{3})\) and \(\cos^{-1}(\frac{\pi}{3})\) are not defined.

Since \(\sin^{-1}(\frac{\pi}{3})\) and \(\cos^{-1}(\frac{\pi}{3})\) do not exist, the entire expression does not exist.

Thus, the correct option is (D) Does not exist.