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If sin(x +3alpha)=3 sin (alpha-x), then...

If `sin(x +3alpha)=3 sin (alpha-x)`, then

A

`tan x = tan alpha`

B

`tan x = tan^(2)alpha`

C

`tan x = tan^(3)alpha`

D

`tan x=3 tan alpha`

Text Solution

Verified by Experts

The correct Answer is:
C
`sin (x+3alpha)=3 sin (alpha - x)`
`rArr sin x cos 3alpha + sin 3 alpha cos x = 3 (sin alpha cos x - sin x cos alpha)`
`rArr sin x(cos 3alpha + 3 cos alpha) = cos x(3 sin alpha - sin 3 alpha)`
`rArr tan x = (4sin^(3)alpha)/(4 cos^(3)alpha)=tan^(3)alpha`
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