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If cos-1x+cos-1y+cos-1z=pi and x+y+z=3/2, prove that x=y=z. Please help....urgent.

If cos-1x+cos-1y+cos-1z=pi and x+y+z=3/2, prove that x=y=z. Please help....urgent.

Grade:12

1 Answers

Diwesh Joshi
11 Points
3 years ago
or, cos-1x+cos-1y+cos-1z=πor, cos-1(xy-√(1-x²)(1-y²)=π-cos-1zor, xy-√(1-x²)(1-y²)=cos(π-cos-1z)or, xy-√(1-x²)(1-y²)=-cos(cos-1z)or, xy-√(1-x²)(1-y²)=-zor, xy+z=xy-√(1-x²)(1-y²)Squaring on both sides,or, x²y²+2xyz+z²=(1-x²)(1-y²)or, x²y²+2xyz+z²=1-y²-x²+x²y²or, 2xy+z²=-y²-z²+1Therefore, x²+y²+z²+2xyz=1

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