Q: If 3 sinβ = sin(2α+ β), then tan(α+ β) is equal to
(A) 2 tanβ
(B) 2 tanα
(C) tanα + tanβ
(D) none of these
Sol. $\large \frac{sin(2\alpha + \beta)}{sin\beta} = \frac{3}{1}$
$\large \frac{sin(2\alpha + \beta) + sin\beta}{sin(2\alpha + \beta) – sin\beta} = \frac{3+1}{3-1} = 2 $
$\large \frac{2 sin(\alpha + \beta) cos\alpha}{2sin\alpha cos(\alpha + \beta)} = 2$
⇒ tan(α + β) = 2 tanα
Hence (B) is the correct answer.
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