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  • If x,y,z belong [-1,1] such that cos^-1 x+cos^-1 y+cos^-1 z=3pi, then find the value of xy+yz+zx .

If x,y,z belong [-1,1] such that cos^-1 x+cos^-1 y+cos^-1 z=3pi, then find the value of xy+yz+zx .

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Solution:   We have ,      x,y,zin[-1,1]

           -1leq xleq 1   ,   -1leq yleq 1 ,  -1leq zleq 1

    0leq cos^-1xleq pi  ,   0leq cos^-1yleq pi  ,   0leq cos^-1zleq pi

     Rightarrow        cos^-1x+cos^-1y+cos^-1z=3pi

    Rightarrow          x=y=z=-1  Rightarrow   xy+yz+zx=3

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Deependra Verma

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