Question

Solve : Sin²θ - 3sin θ + 2 = 0 .

Answer 1

sin²θ - 3sin θ + 2 = 0
⇒ sin²θ - 2sin θ - sin θ + 2 = 0
⇒ sin θ (sin θ - 2) - 1(sin θ - 2) = 0
⇒ (sin θ - 2)(sin θ - 1) = 0
⇒ sin θ - 2 = 0
⇒ sin θ = 2

sin θ = 2 has no solution for angle θ, as there is no any angle whose sin θ is equal to 2.
⇒ sin θ - 1 = 0
⇒ sin θ = 1
⇒ θ = 90°