Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.) sin ( x + π /2) − cos^2 x = 0

Answer 1

sin[x+(π/2)] = sin x cos π/2 + cos x sin π/2 = cos x

cos x - cos²x = 0 => cos x = 0 and 1 - cos x = 0, i.e. cos x = 1

With that information you can get the values you need.