To solve the equation cos²x + sin x = 1, we can use the trigonometric identity cos²x = 1 - sin²x. By substituting this identity into the equation, we get:
1 - sin²x + sin x = 1
Combining like terms, we get:
1 - sin²x = 0
Solving for sin x, we get:
sin x = 1
However, the sine function has a range of [-1, 1], so the only solution in the interval [0, 2π] is sin x = 1, which corresponds to x = π/2. So the solution to the equation cos²x + sin x = 1 in the interval [0, 2π] is x = π/2.