Question

cos 2x - 5 sin x - 3 = 0
prove that

Answer 1

⇒1 - 2 sin2x - 5 sin x - 3 = 0⇒2 sin2x + 5 sin x + 2 = 0⇒2 sin2x + 4 sin x + sin x + 2 = 0⇒2 sin x (sin x + 2) + 1(sin x + 2) = 0⇒(2 sin x + 1)(sin x + 2) = 0⇒2 sin x + 1 = 0   or  sin x + 2 = 0⇒sin x = -1/2   or  sin x = -2  [rejected]⇒sin x = -1/2⇒sin x = - sin(π/6)⇒sin x = sin(π+π/6)⇒sin x = sin(7π/6)⇒x = nπ + (-1)n(7π/6)   , where n ∈ Z

Answer 2

Hope this àns is correct