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

Question

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

Tardigrade Admin · Accepted Answer

Given, sin θ =3 sin (θ +2α ) ⇒ ( sin θ / sin (θ +2α ))=(3/1) Use componendo and dividendo formula, =( sin θ + sin (θ +2α )/ sin θ - sin (θ +2α ))=(3+1/3-1) =-(2 sin (θ +α ). cos α /2 cos (θ +α ). sin α )=2 ⇒ - tan (θ +α ). cot α =2 ⇒ tan (θ +α )=-2 tan α ⇒ tan (θ +α )=2 tan α =0

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

$3$

$2$

$- 1$

$0$

$1$

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

3

2

−1

0

1

Given, sinθ=3sin(θ+2α) ⇒ sin(θ+2α)sinθ​=13​ Use componendo and dividendo formula, =sinθ−sin(θ+2α)sinθ+sin(θ+2α)​=3−13+1​ =−2cos(θ+α).sinα2sin(θ+α).cosα​=2 ⇒ −tan(θ+α).cotα=2 ⇒ tan(θ+α)=−2tanα ⇒ tan(θ+α)=2tanα=0

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

$3$

$2$

$- 1$

$0$

$1$