Question

Find the general solution of the following equation:

sin θ = tan θ.

Answer 1

sin θ = tan θ
∴ sinθ = `"sinθ"/"cosθ"`
∴ sinθ cosθ = sinθ
∴ sinθ cosθ – sinθ = 0
∴ sinθ (cosθ – 1) = 0
∴ either sinθ = 0 or cosθ – 1 = 0
∴ either sinθ = 0 or cosθ = 1
∴ either sinθ = 0 or cosθ = cos0  ...[∵ cos 0 = 1]

The general solution of sin θ = 0 is θ = nπ, n ∈ Z and  cosθ = cos α is θ = 2nπ ± α, where n ∈ Z.

∴ the required general solution is given by
θ = nπ, n ∈ Z or θ = 2nπ ± 0, n ∈ Z
∴ θ = nπ, n ∈ Z or θ = 2nπ, n ∈ Z.