KCET · Maths · Matrices
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 & Solution
Correct Answer
(D) Does not exist
Step-by-step Solution
Detailed explanation
We have, \(\cos \left(\sin ^{-1} \frac{\pi}{3}+\cos ^{-1} \frac{\pi}{3}\right)\) \(\sin ^{-1} x\) is defined \(x \in[-1,1]\)
\(\begin{aligned}
&\text { but } \frac{\pi}{3} \notin[-1,1] \\
&\therefore \cos \left(\sin ^{-1}\left(\frac{\pi}{3}\right)+\cos ^{-1}\left(\frac{\pi}{3}\right)\right) \text { does not exists. }
\end{aligned}\)
\(\begin{aligned}
&\text { but } \frac{\pi}{3} \notin[-1,1] \\
&\therefore \cos \left(\sin ^{-1}\left(\frac{\pi}{3}\right)+\cos ^{-1}\left(\frac{\pi}{3}\right)\right) \text { does not exists. }
\end{aligned}\)
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