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  • If x,y,z belong [-1,1] such that cos^-1 x+ cos^-1 y+cos^-1 z=0, find x+y+z.

If x,y,z belong [-1,1] such that cos^-1 x+ cos^-1 y+cos^-1 z=0, find x+y+z.

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Solution:      We have ,

                   x,y,zin[-1,1].

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

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

          herefore       cos^-1x+cos^-1y+cos^-1z=0

  Rightarrow      cos^-1x=0  ,cos^-1y=0  ,  cos^-1z=0

 Rightarrow            x=y=z=1

Hence ,    x+y+z=3.

Posted by

Deependra Verma

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