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If A+B+C=pi, prove that (tanA)/(tanBdot...

If `A+B+C=pi,` prove that `(tanA)/(tanBdottanC)+(tanB)/(tanAdott a n C)+(tanC)/(tanAdottanB)tanA+tanB+tanC-2cot A-2cot B-2cot C`

Text Solution

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`=(tan ^(2)A+tan^(2)B+tan^(2)C)/(tanA.tan B. tanC)`
`(tan A+tan B+tanC)^(2)-2(tan A tan B+tan B tan C
(+tanC. tanA")") / (tan A. tan B. tan C)`
`2(tan A. tan B+tan B tan C`
`=((tan A+tan B+tanC)^(2))/(tan A + tan B + tan C) - (+tan C.tanA)/(tan A. tan B. tan C)`
`(because tan A+tan B+tan C=tan A tan B tan C`
`=tan A+tan B+tan C-2 cot A-2 cot B-2 cot C`
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