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

  • question_answer
    The sum of the solutions of the equation\[2{{\sin }^{-1}}\sqrt{{{x}^{2}}+x+1}+{{\cos }^{-1}}\sqrt{{{x}^{2}}+x}=\frac{3\pi }{2}\]is

    A) 0         

    B) -1

    C) 1                     

    D) 2

    Correct Answer: B

    Solution :

    [b] \[0\le {{x}^{2}}+x+1\le 1\]and \[0\le {{x}^{2}}+x+\le 1\] \[\therefore x=-1,0\] For \[x=-1\] L.H.S.\[=2{{\sin }^{-1}}1+{{\cos }^{-1}}0=\frac{3\pi }{2}\] \[\therefore x=-1\] is a solutions. For \[x=0,\]L.H.S.\[=2{{\sin }^{-1}}1+{{\cos }^{-1}}0=\frac{3\pi }{2}\] Therefore, \[x=0\] is a solution and sum of the solutions\[=-1\].


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