What is the solution for the equation tan θ = tan α ?

1.	What is the solution for the equation tan θ = tan α ?
Answer» tan θ = tan α ⇒ \(\frac{sin\,\theta}{cos \,\theta}\) = \(\frac{sin\,\alpha}{cos \,\alpha}\) ⇒ sin θ cos α - cos θ sin α = 0 ⇒ sin (θ - α) = 0 ⇒ θ – α = nπ ⇒ θ = nπ + α, n∈I.

Answer»

tan θ = tan α

⇒ \(\frac{sin\,\theta}{cos \,\theta}\) = \(\frac{sin\,\alpha}{cos \,\alpha}\)

⇒ sin θ cos α - cos θ sin α = 0

⇒ sin (θ - α) = 0

⇒ θ – α = nπ

⇒ θ = nπ + α, n∈I.

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