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

  • question_answer
    The number of integer x satisfying \[{{\sin }^{-1}}\left| x-2 \right|+{{\cos }^{-1}}(1-\left| 3-x \right|)=\frac{\pi }{2}\] is

    A) 1                     

    B) 2

    C) 3         

    D) 4

    Correct Answer: B

    Solution :

    [b] \[{{\sin }^{-1}}\left| x-2 \right|+{{\cos }^{-1}}(1-\left| 3-x \right|)=\frac{\pi }{2}\] Or \[\left| x-2 \right|=1-\left| 3-x \right|\] Or \[\left| x-2 \right|+\left| 3-x \right|=\left| (x-2)+(3-x) \right|\] Or \[(x-2)(3-x)\ge 0\] Or \[2\le x\le 3\]


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