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JEE Main & Advanced Mathematics Inverse Trigonometric Functions Question Bank Mock Test - Inverse Trigonometric Functions

  • question_answer
    \[f(x)=ta{{n}^{-1}}x+{{\tan }^{-1}}\left( \frac{1}{x} \right);g(x)=si{{n}^{-1}}x+co{{x}^{-1}}x\]are identical functions if

    A) \[x\in R\]           

    B) \[x>0\]

    C) \[x\in [-1,1]\]     

    D) \[x\in (0,1]\]

    Correct Answer: D

    Solution :

    [d] \[\left( \frac{\pi }{2}-2x \right)=\cos 6x=\left\{ \begin{matrix}    \frac{\pi }{2}x>0  \\    \frac{-\pi }{2}x<0  \\ \end{matrix} \right.\] \[{{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2}\forall x\in [-1,\,\,1]\].


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