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If alpha+beta+gamma=2pi, then tanalpha/...

If `alpha+beta+gamma=2pi,` then `tanalpha/2tanbeta/2+tangamma/2=tanalpha/2tanbeta/2tangamma/2` `tanalpha/2tanbeta/2+tanbeta/2tangamma/2+tangamma/2tanalpha/2=1` `tanalpha/2+tanbeta/2+tangamma/2=-tanalpha/2tanbeta/2tangamma/2` none of these

A

`tan.(alpha)/(2)+tan.(beta)/(2)+tan.(gamma)/(2)=tan.(alpha)/(2)tan.(beta)/(2)tan.(gamma)/(2)`

B

`tan.(alpha)/(2)tan.(beta)/(2)+tan.(beta)/(2)tan.(gamma)/(2)+tan.(gamma)/(2)tan.(alpha)/(2)=1`

C

`tan.(alpha)/(2)+tan.(beta)/(2)+tan.(gamma)/(2)=-tan.(alpha)/(2)tan.(beta)/(2)tan.(gamma)/(2)`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
a
Since, `(alpha)/(2) + (beta)/(2) = (pi - (gamma)/(2))`
`therefore tan ((alpha)/(2)+(beta)/(2))=tan(pi-(gamma)/(2))`
`implies (tan.(alpha)/(2)+tan.(beta)/(2))/(1-tan.(alpha)/(2)tan.(beta)/(2))=-tan.(gamma)/(2)`
`impliestan.(alpha)/(2)+tan.(beta)/(2)+tan.(gamma)/(2)=tan.(alpha)/(2)tan.(beta)/(2)tan.(gamma)/(2)`
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