Q. The value of $\sin\left\lbrack \frac{\pi}{2} - \sin^{- 1}\ \left( - \frac{\sqrt{3}}{2} \right) \right\rbrack$ is
A) $\frac{\sqrt{3}}{2}$
B) $- \frac{\sqrt{3}}{2}$
C) $\frac{1}{2}$
D) $- \frac{1}{2}$
Explanation
(c)
$\sin\left\lbrack \frac{\pi}{2} - \sin^{- 1}\left( - \frac{\sqrt{3}}{2} \right) \right\rbrack = \cos{\sin^{- 1}\left( \frac{\sqrt{3}}{2} \right)}$
$= \cos{\cos^{- 1}\sqrt{1 - \frac{3}{4}}}$
$= \cos{\cos^{- 1}{\left( \frac{1}{2} \right) = \frac{1}{2}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.