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If 3 sin beta= sin( 2alpha+beta), then...

If `3 sin beta= sin( 2alpha+beta)`, then

A

`2tan beta`

B

`2tan alpha`

C

`tan alpha+tan beta`

D

`tan alpha`

Text Solution

Verified by Experts

The correct Answer is:
B
If `3 sin beta = sin` …………
`(sin(2alpha+beta))/(sin beta) = (3)/(1)`
`implies (sin(2alpha+beta))/(sin(2alpha+beta)-sin beta)`
`= (3+1)/(3-1) = (4)/(2) = 2`
`implies (2sin(alpha+beta)cos alpha)/(2sin alpha sin(alpha+beta)) = 2`
`implies tan (alpha+beta) = 2 tan alpha`.
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