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Discussion Forum



1)

The value of  $\sin^{-1}\left(\frac{1}{2}\right)+\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$  is


A) $\cos^{-1}\left(\frac{1}{2}\right)$

B) $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

C) $\cos^{-1}\left(-\frac{1}{2}\right)$

D) $\sin^{-1}\left(-\frac{1}{2}\right)$

Answer:

Option C

Explanation:

 we have,

 $\sin^{-1}\left(\frac{-1}{2}\right)+\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

$-\sin^{-1}\left(\frac{1}{2}\right)+\pi-\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$

$=-\frac{\pi}{6}+\pi-\frac{\pi}{6}=\pi-\frac{\pi}{3}=\frac{2\pi}{3}=\cos^{-1}(\frac{-1}{2})$