Final answer:
To find the exact solutions of the equation sin^2 x + 3cos x - 1 = 2, rearrange the equation to sin^2 x + 3cos x - 3 = 0. Solve the quadratic equation in terms of cos x. Substitute the values of cos x back into the original equation to find the solutions for x.
Step-by-step explanation:
To find the exact solutions of the equation sin^2 x + 3cos x - 1 = 2, we can rearrange the equation to sin^2 x + 3cos x - 3 = 0. This is a quadratic equation in terms of cos x. We can solve it by factoring or by using the quadratic formula. Once we find the possible values of cos x, we can substitute them back into the original equation to find the corresponding values of x.