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If A + B + C = 180^(@), then prove that ...

If A + B + C = `180^(@)`, then prove that tan A + tan B + tan C = tan A tan B tan C.

Text Solution

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Since, A + B = `180^(@)C`
`therefore tan(A + B) = tan(180^(@)-C)`
`implies (tanA+tanB)/(1-tanAtanB)=-tanC`
`implies tanA + tanB =- tan C + tan A tan B tan C`
`implies tanA + tanB +tanC = tanA tanB tanC`
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