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JEE Main & Advanced Mathematics Inverse Trigonometric Functions Question Bank Inverse trigonometric functions

  • question_answer
    If \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi ,\]then \[xy+yz+zx=\] [Karnataka CET 2003]

    A) 0

    B) 1

    C) 3

    D) -3

    Correct Answer: C

    Solution :

     Given \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi \] \[\because 0\le {{\cos }^{-1}}x\le \pi \] \[\therefore 0\le {{\cos }^{-1}}y\le \pi \]and \[0\le {{\cos }^{-1}}z\le \pi \] Here \[{{\cos }^{-1}}x={{\cos }^{-1}}y={{\cos }^{-1}}z=\pi \] \[\Rightarrow x=y=z=\cos \pi =-1\] \ \[xy+yz+zx\]\[=(-1)(-1)+(-1)(-1)+(-1)(-1)\]                               \[=1+1+1=3\].


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