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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

3

B

2

C

-1

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`because(sintheta)/(sin(theta+2alpha))=(3)/(1)`
On applying componendo and dividendo rule, we get
`(sintheta+sin(theta+2alpha))/(sintheta-sin(theta+2alpha))=(3+1)/(3-1)`
`implies-(2sin(theta+alpha)cosalpha)/(2cos(theta+alpha)sinalpha)=2`
`implies-tan(theta+alpha)cotalpha=2`
`implies tan(theta+alpha)+2tanalpha=0`
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