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In trangle ABC Cos 2 A +cos 2 B+cos 2 C=cosB×cosC+cosC×cosA+cosA×cosB Then prove triangle are equilateral.

In trangle ABC Cos2A +cos2B+cos2C=cosB×cosC+cosC×cosA+cosA×cosB
Then prove triangle are equilateral.

Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
5 years ago
let cosA=x, cosB=y, cosC=z
the given qn then becomes
x^2+y^2+z^2-xy-yz-zx=0
or ((x-y)^2+(y-z)^2+(z-x)^2)/2=0
this can only equal zero if x-y=y-z=z-x=0
or, x=y=z
or cosA=cosB=cosC

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