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

Question

If sinθ = 3sin(θ + 2α), then the value of tan(θ + α) + 2tanα is (A) 3 (B) 2 (C) -1 (D) 0

Tardigrade Admin · Accepted Answer

sinθ = 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=4 cos(θ+α)sinα ⇒ (-sin(θ+α)/cos(θ+α))=(2 sin α/cos α) ⇒ tan(θ + α) + 2tanα = 0

Q. If $s in θ = 3 s in (θ + 2 α)$ , then the value of
$t an (θ + α) + 2 t an α$ is

$3$

$2$

$- 1$

$0$

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

3

2

−1

0

sinθ=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 ⇒cos(θ+α)−sin(θ+α)​=cosα2sinα​ ⇒tan(θ+α)+2tanα=0

Q. If $s in θ = 3 s in (θ + 2 α)$ , then the value of
$t an (θ + α) + 2 t an α$ is

$3$

$2$

$- 1$

$0$