Question

If sinθ = 3sin(θ + 2α), then the value of tan (θ + α) + 2tanα is

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

Answer: (D)

0

Answer 2

Given that sin θ = 3sin (θ + 2α)

⇒ sin (θ + α − α) = 3sin (θ + α + α) ⇒ sin (θ +α)

cosα –cos(θ + α) sinα =3sin (θ + α) cosα + 3cos (θ + α) sinα ⇒ –2sin (θ + α) cosα = 4cos (θ + α) sinα

⇒$\frac{- \sin(\theta + \alpha)}{\cos(\theta + \alpha)} = \frac{2\sin\alpha}{\cos\alpha}$⇒ tan(θ+α) + 2tanα = 0