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In a DeltaABC, prove that : tanA+tanB+ta...

In a `DeltaABC`, prove that : `tanA+tanB+tanC= tanA tanB tanC`

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In `DeltaABC`,
`A+B+C=180^(@)`
`rArr A+B=180^(2)-C`
`rArr tan(A+B)=tan(180^(@)-C)`
`rArr (tanA+tanB)/(1-tanAtanB)=-tanC`
`rArr tanA+tanB=-tanC+tanAtanBtanC`
`rArr (sinA)/(cosA)+(sinB)/(cosB)+(sinC)/(cosC)=(sinA)/(cosA).tanBtanC`
`rArr (ksinA)/(cosA)+(ksinB)/(cosB_+(sinC)/(cosA).tanBtanC`
`rArr (ksinA)/(cosA)+(ksinB)/(cosB)+(ksinC)/(cosC)=(ksinA)/(cosA).tanBtanC`
`rArr asecA+bsecA+csecC=asecA tanB tanC`. Hence Proved.
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