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If tantheta+tan2theta+sqrt(3)tanthetatan...

If `tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3)`, then `theta=(npi)/(3)+(pi)/(9)`.

A

`theta=((3=6n+1)pi)/(18)AAninI`

B

`theta=((6n+1)pi)/(9),AAninI`

C

`theta=((3n+1)pi)/(9),AAninI`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`becausetan2theta+sqrt(3)tanthetatan2theta=sqrt(3)`
`rArrtantheta+tan2theta=sqrt(3)(1-tanthetatan2theta)`
`rArr(tantheta+tan2theta)/(1-tanthetatan2theta)=sqrt(3)rArrtan3theta="tan"(pi)/(3)`
`rArr3theta=npi+(pi)/(3)rArrtheta=((3n+1)pi)/(9),AAninI`
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