given equation is sin2x + cos x= 0

⇒ 2 sin x cos x + cos x = 0 (∵ sin 2A = 2 sin A cosA)

⇒ cos x (2 sin x + 1) = 0

⇒ cos x = 0 or 2sin x +1 = 0

Now cos x = 0

⇒

And 2 sin x + 1= 0

⇒

⇒

∴ the general solution of the equation is