Question

sin theta = 3sin (theta + 2 alpha) then prove that tan (theta + alpha) +2tan alpha= 0
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Answer 1

Answer:

ANSWER

sinθ=3sin(θ+2α)

⇒3sin(θ+α+α)=sinθ

3sin(θ+α)cosα+3cos(θ+α)sinα=sin(θ+α−α)

3sin(θ+α)cosα+3cos(θ+α)sinα=sin(θ+α)cosα−sinαcos(θ+α)

2sin(θ+α)cosα=−4cos(θ+α)sinα

2tan(θ+α)=−4tanα

tan(θ+α)=−2tanα

⇒tan(θ+α)+2tanα=0

Hence, the answer is 0.