Apply Pythagorean Identity

\sin^2x+\cos^2x=1

Transform

2 \sin x + \cos^2x = 2

to the following equation

\sin^2x- 2 \sin x+1 = 0

Factor the equation

(\sin x-1)^2 = 0

Solve the equation

\sin x = 1

or

x = \dfrac{\pi}{2}+2k\pi

where k is any integer.