The value of $cot^{-1}\left[2cos\left(2sin^{-1}\frac{1}{2}\right)\right]$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{\pi}{4}$
$\cot^{-1}\left[2\cos\left(2\sin^{-1}\frac{1}{2}\right)\right]$
$=\cot^{-1}\left(2\cos\left(2×\frac{π}{6}\right)\right)$
$=\cot^{-1}(2×\frac{1}{2})=\cot^{-1}(1)$
$=\frac{\pi}{4}$