Question

Find the general solution of the equation sin x = tan x.

Answer 1

sin x = tan x
∴ sin x = sinx/cosx
∴ sin x cos x - sin x = 0
∴ sin x (cos x - 1) = 0 
∴ sin x = 0 or cos x = 1
∴ sin x = sin 0 or cos x = cos 0

Since, sin θ = 0 implies θ = nπ and cos θ = cos α implies θ = 2nπ±α  , n ∈ Z.
∴ x = nπ or x = 2mπ ± 0
∴ the required general solution is x = nπ or x = 2mπ, where n, m ∈ Z.