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In DeltaABC, prove that: tanA/2tanB/2+...

In `DeltaABC`, prove that:
`tanA/2tanB/2+tanB/2tanC/2+tanC/2tanA/2=1`

Text Solution

Verified by Experts

We have,
`A+B+C=pi`
`rArr (A+B)/(2) = (pi-C)/(2)`
`rArr tan(A+B)/(2) = tan(pi-C)/(2)`
`rArr (tanA/2+tanB/2)/(1-tanA/2. tanB/2)=cot C/2`
`rArr (tanA/2+tanB/2)/(1-tanA/2.tanB/2)=1/(tanC/2)`
`rArr tanA/2. tanC/2+tanB/2.tanC/2=1-tanA/2.tanB/2`
`rArr tanA/2.tanB/2 +tanC/2 + tanC/2.tanA/2=1`
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AAKASH INSTITUTE-TRIGNOMETRIC FUNCTIONS -Section - J (Akash Challengers Question)
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