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If tan(alpha+beta)=2andtan (alpha-beta)...

If `tan(alpha+beta)=2andtan (alpha-beta)=1`, then `tan(2alpha)` is equal to

A

`-3`

B

`-2`

C

`(1)/(3)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
`tan(alpha+beta)=2`
`tan(alpha-beta)=1`
`tan2alpha=tan[(alpha+beta)+(alpha-beta)]`
`=(tan(alpha+beta)+tan(alpha-beta))/(1-tan(alpha+beta).tan(alpha-beta))`
`=(2+1)/(1-2.1)=(3)/(-1)=-3`
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