Final answer:
The equation cos^2(x) = 5sin(x) is solved by using trigonometric identities and constraints of the interval 0 ≤ x < 2π. After substitution and solving the quadratic, we find that none of the multiple-choice options provided satisfy the equation within the given interval.
Step-by-step explanation:
The equation cos^2(x) = 5sin(x) can be solved by using trigonometric identities and by examining the solutions within the interval 0 ≤ x < 2π. To solve this, we can use the identity sin^2(x) + cos^2(x) = 1, which implies cos^2(x) = 1 - sin^2(x). We then substitute 1 - sin^2(x) for cos^2(x) in the equation and solve for sin(x). This yields a quadratic equation in terms of sin(x) which can be factored or solved using the quadratic formula. The solutions for x must fall within the given interval and satisfy the initial equation.
None of the options a) x = π/2, b) x = π, c) x = 3π/2, or d) x = 2π are correct because when we plug these values into either side of the equation, they do not create equality. In particular, cos^2(x) for these values will either be 0 or 1, and none of these values when plugged into 5sin(x) will satisfy the equation cos^2(x) = 5sin(x).