Q112 / 180 · KCET 2020 · Mathematics

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

  • A
    0
  • B
    1
  • C
    $-0$
  • Correct answer
    D
    Does not exist

Solution

We have, $\cos \left(\sin ^{-1} \frac{\pi}{3}+\cos ^{-1} \frac{\pi}{3}\right)$ $\sin ^{-1} x$ is defined $x \in[-1,1]$ $\begin{aligned} &\text { but } \frac{\pi}{3} \notin[-1,1] \\ &\therefore \cos \left(\sin ^{-1}\left(\frac{\pi}{3}\right)+\cos ^{-1}\left(\frac{\pi}{3}\right)\right) \text { does not exists. } \end{aligned}$

Hence, the correct answer is option: 'D'.

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