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Question

If x+y+z=xyz, prove that x+y1xy+y+z1yz+z+x1zx=x+y1xyy+z1yzz+x1zx.

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Solution

As above A+B+C=0 or nπ
tanA+tanB+tanC=tanAtanBtanC ..(1)
Now A=π(B+C)
tanA=tan(B+C)
or tanA=tanB+tanC1tanBtanC=(y+z1yz) etc.
Now put in (1) and cancel ive sign from both sides.
x+y1xy+y+z1yz+z+x1zx=x+y1xyy+z1yzz+x1zx.

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