A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{6}\]
C) \[\frac{2\pi }{3}\]
D) \[-\frac{\pi }{3}\]
Correct Answer: C
Solution :
\[{{\cos }^{-1}}\left( \sin \frac{7\pi }{6} \right)={{\cos }^{-1}}\left[ \sin \left( 2\pi -\frac{5\pi }{6} \right) \right]\] \[={{\cos }^{-1}}\left[ -\sin \frac{5\pi }{6} \right]\] \[={{\cos }^{-1}}\left[ -\sin \left( \frac{\pi }{2}+\frac{\pi }{3} \right) \right]\] \[={{\cos }^{-1}}\left[ -\cos \frac{\pi }{3} \right]\] \[=\pi -\frac{\pi }{3}=\frac{2\pi }{3}\]
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