cos^2(x) + sin(x) = 1

Question

- Find all solutions in the interval [0, 2pi)

I got pi/2 but the answer says {0, pi/2, pi}

Where does 0 and pi come from for solutions? When simplifying I just get sin(x)=1

Answer 1

If x = 0
cos^2 0 = 1 and sin 0 = 0 and 1+0 =1

If x = pi
cos^2 pi = (-1)(-1) = 1 and sin pi = 0 so 1+0 = 1 again

Answer 2

776