cosx=-sin^2 x-1 find all solution in interval [0,2pi) CAN SOMEONE PLEASE HELP ME FOR THIS QUESTION

Question

cosx=-sin^2 x-1 find all solution in interval [0,2pi)

CAN SOMEONE PLEASE HELP ME FOR THIS QUESTION

Answer 1

cosx = - (1 - cos²x) - 1, cos²x - cosx - 2 = 0, or (cosx - 2)(cosx + 1) = 0

From here cosx = 2 (no solutions) or cosx = -1, x = π

Answer: x = π only solution of this equation on interval [0, 2π)