Find all solutions of the equation in the interval [0,2pi] algebraically.

Question

sin^2x + cosx + 1 = 0

Answer 1

(1-cos^2 x) + cos x + 1 = 0
- cos^2 x + cos x + 2 = 0

cos^2 x - cos x - 2 = 0

(cos x - 2)(cos x + 1) = 0
cos x = 2 impossible, out of range
so
cos x = -1
pi