A) \[-\frac{\pi }{3}\]
B) \[\frac{\pi }{6}\]
C) \[-\frac{\pi }{4}\]
D) \[\frac{\pi }{4}\]
E) \[\frac{\pi }{2}\]
Correct Answer: C
Solution :
\[{{\sin }^{-1}}\{\cos (4095{}^\circ )\}\] \[={{\sin }^{-1}}\{\cos (11.360{}^\circ +135{}^\circ )\}\] \[={{\sin }^{-1}}\{\cos (135{}^\circ )\}\] \[=\sin \left\{ \cos \left( \frac{\pi }{2}+\frac{\pi }{4} \right) \right\}\] \[={{\sin }^{-1}}\left( -\sin \frac{\pi }{4} \right)\] \[={{\sin }^{-1}}\left( -\frac{1}{\sqrt{2}} \right)=-\frac{\pi }{4}\]
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