If 3sinbeta=sin(2alpha+beta) then tan(a...

If `3sinbeta=sin(2alpha+beta)` then `tan(alpha+beta)-2tanalpha` is (a)independent of `alpha` (b)independent of `beta` (c)dependent of both `alpha` and `beta` (d)independent of both `alpha` and `beta`

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`tan(alpha+beta) - 2tanalpha`
`= sin(alpha+beta)/cos(alpha+beta) - sinalpha/cosalpha - tanalpha`
`=(sin(alpha+beta)cosalpha - sinalphacos(alpha+beta))/(cosalphacos(alpha+beta)) - tanalpha`
`=(sin(alpha+beta-alpha))/(cosalphacos(alpha+beta)) - sinalpha/cosalpha`
`=(sinbeta)/(cosalphacos(alpha+beta)) - sinalpha/cosalpha`
`=(sinbeta - sinalphacos(alpha+beta))/(cosalphacos(alpha+beta)) `
`=(2(sinbeta - sinalphacos(alpha+beta)))/(2cosalphacos(alpha+beta)) `
`=(2sinbeta - 2sinalphacos(alpha+beta))/(2cosalphacos(alpha+beta)) `
...

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