The value of \(\sin^{-1}\left[\cos\left(\sin^{-1}\displaystyle\frac{\sqrt{3}}{2}\right)\right]\) is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{\pi}{6}\)
The principal value branch of \(\sin^{-1}\) is \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\). Working from the inside out:
\( \displaystyle \sin^{-1}\frac{\sqrt{3}}{2} = \frac{\pi}{3} \)
\( \displaystyle \cos\frac{\pi}{3} = \frac{1}{2} \)
\( \displaystyle \sin^{-1}\frac{1}{2} = \frac{\pi}{6} \)