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If tanalpha+tanbeta+tangamma=tanalphatan...

If `tanalpha+tanbeta+tangamma=tanalphatanbetatangamma,then`

A

`alpha, beta` must be angles of a triangle

B

the sum of any two of `alpha, beta,gamma` is equal to the third

C

`alpha+beta+gamma` must be an integral multiple of `pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`tanalpha+tanbeta+tangamma=tanalpha tanbetatangammaBut, tan(alpha+beta+gamma)`
`=(tanalpha+tanbeta+tangamma-tanalphatanbetatangamma)/(1-tanalphatanbeta-tanbetatangamma-tangamma tanalpha)`
`thereforetan(alpha+beta+gamma)=0impliesalpha+beta+gamma=npi, n inZ`
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