JEE Main & Advanced JEE Main Paper (Held On 22 April 2013)

  • question_answer
    The number of solution of the equation, \[{{\sin }^{-1}}\] \[x=2\] \[{{\tan }^{-1}}\] \[x\] (in principal values is :)     JEE Main  Online Paper (Held On 22 April 2013)

    A)  1                                            

    B)  4

    C)  2                                            

    D)  3

    Correct Answer: A

    Solution :

     Given equation is \[{{\sin }^{-1}}x=2{{\tan }^{-1}}x\] Now, this equation has only one  solutioin. \[\therefore \]  \[LHS={{\sin }^{-1}}1=\frac{\pi }{2}\] and \[RHS=2{{\tan }^{-1}}1=2\times \frac{\pi }{4}=\frac{\pi }{2}\] Also, \[x=1\]gives angle value as \[\frac{\pi }{4}\]and \[\frac{5\pi }{4}\] \[\frac{5\pi }{4}\]is outside the principal value.

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