Simplified value of sin[π/2 - sin⁻¹(-(√3)/2)] is:

Simplified value of $\sin\left[\frac{\pi}{2} - \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right]$ is:

(a)$\frac{1}{2}$
(b)$\frac{1}{\sqrt{2}}$
(c)$\frac{\sqrt{3}}{2}$
(d)$-\frac{\sqrt{3}}{2}$

Answer

Correct option: (a)

Answer: (a) $\frac{1}{2}$ $\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right) = -\frac{\pi}{3}$, so the expression is $\sin\left(\frac{\pi}{2} + \frac{\pi}{3}\right) = \cos\frac{\pi}{3} = \frac{1}{2}$.