Question

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

Options

• 3

• 2

• – 1

• 0

Answer 1

If sin θ = 3 sin (θ + 2α), then the value of tan (θ + α) + 2 tan α is 0.

Explanation:

∵ `sinθ/(sin(θ + 2α)) = 3/1`

On applying componendo arid dividendo rule, we get

`(sin θ + sin (θ + 2α))/(sin θ - sin (θ + 2α)) = (3 + 1)/(3 - 1)`

`\implies - (2 sin (θ + α) cos α)/(2 cos (θ + α) sin α)` = 2

`\implies` – tan (θ + α) cot α = 2

`\implies` tan (θ + a) + 2 tan α = 0