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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

  • question_answer
    If \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi \] then\[xy+yz+zx\] is equal to :

    A)  1                                            

    B)  0

    C)  -3                                          

    D)  3

    Correct Answer: D

    Solution :

    Here we have \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi \] and we know that \[0\le {{\cos }^{-1}}x\le \pi \] \[\therefore \] we have \[{{\cos }^{-1}}x=\pi ,\,{{\cos }^{-1}}y=\pi ,\,{{\cos }^{-1}}z=\pi \] \[\therefore \]  \[x=y=z=\cos \pi =-1\] \[\therefore \] \[xy+yz+zx=(-1)\,(-1)+(-1)\,(-1)\]                                                                 \[+\,(-1)\,(-1)\]                 \[=1+1+1=3\]


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