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JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer
    If\[x=1/5\]¸the value of\[\cos ({{\cos }^{-1}}x+2{{\sin }^{-1}}x)\]is

    A) \[-\sqrt{\frac{24}{25}}\]                    

    B) \[\sqrt{\frac{24}{25}}\]

    C) \[-\frac{1}{5}\]                                  

    D) \[\frac{1}{5}\]

    Correct Answer: C

    Solution :

     The given expression is equal to             \[\cos ({{\cos }^{-1}}x+{{\sin }^{-1}}x+{{\sin }^{-1}}x)\] \[=\cos \left( \frac{\pi }{2}+{{\sin }^{-1}}x \right)=-\sin ({{\sin }^{-1}}x)=-x=-\frac{1}{5}\] \[[\text{Using}{{\cos }^{-1}}x+{{\sin }^{-1}}x=\frac{\pi }{2}]\]


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