To solve the equation sin²x + cosx - 1 = 0, we can use the trigonometric identity sin²x + cos²x = 1.

Rearranging the equation, we have sin²x + cosx = 1.

Substituting sin²x = 1 - cos²x, we get 1 - cos²x + cosx = 1.

Rearranging further, we have -cos²x + cosx = 0.

Factoring out cosx, we have cosx(-cosx + 1) = 0.

Setting each factor equal to zero, we have cosx = 0 and -cosx + 1 = 0.

Solving cosx = 0, we find x = π/2 + nπ, where n is an integer.

Solving -cosx + 1 = 0, we find cosx = 1, which implies x = 2nπ, where n is an integer.

Therefore, the solutions to the equation sin²x + cosx - 1 = 0 are x = π/2 + nπ and x = 2nπ, where n is an integer.