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If alpha+beta+gamma=2pi, then show that ...

If `alpha+beta+gamma=2pi`, then show that `tan.alpha/2 + tan.beta/2 + tan.gamma/2 = tan.alpha/2 tan.beta/2 tan.gamma/2`.

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

`tan""(alpha)/(2)tan""(beta)/(2)+tan""(beta)/(2)tan""(gamma)/(2)+tan""(gamma)/(2)tan""(alpha)/(2)=0.`

Text Solution

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The correct Answer is:
A
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