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JCECE Engineering JCECE Engineering Solved Paper-2004

  • question_answer
    The value of\[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \cos \frac{5\pi }{3} \right)\]is:

    A) \[10\pi /3\]                        

    B) \[0\]

    C) \[\pi /2\]                                             

    D) \[5\pi /3\]

    Correct Answer: C

    Solution :

    \[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \cos \frac{5\pi }{3} \right)\] \[=\frac{5\pi }{3}+{{\sin }^{-1}}\left[ \sin \left( \frac{\pi }{2}-\frac{5\pi }{3} \right) \right]\]                 \[=\frac{5\pi }{3}+\frac{\pi }{2}-\frac{5\pi }{3}=\frac{\pi }{2}\]


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