How do I solve tan theta=2 sin theta

Answer 1

tanθ - 2sinθ = 0

sinθ/cosθ - 2sinθ = 0

[sinθ - 2sinθcosθ] / cosθ = 0

sinθ(1 - 2cosθ) = 0

sinθ = 0 or cosθ = 1/2

sinθ = 0 when θ = kπ

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ, k = 0, 1, -1, 2, -2, ...