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If sintheta=3sin(theta+2alpha), then th...

If `sintheta=3sin(theta+2alpha)`, then the value of `tan(theta+alpha)+2 tan alpha` is

A

`-1`

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `sintheta=3sintheta=3sin(theta+2alpha)`
`rArr(sin(theta+2alpha))/(sintheta)=(1)/(3)`
Apply componendo and divide do rule
`rArr(sin(theta+2alpha)+sintheta)/(sin(theta+2alpha)-sintheta)=(1+3)/(1-3)`
`rArr(2sin(theta+2alpha)cosalpha)/(2cos(theta+alpha)sinalpha)=(4)/(-2)=-2`
`rArr(tan(theta+alpha))/(tanalpha)=-2`
`rArrtan(theta+alpha)=-2tanalpharArrtann(theta+alpha)+2tanalpha=0`
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