Final answer:
The equation has no solution because it implies sin x = 2, which is impossible since the sine function has a range of [-1, 1].
Step-by-step explanation:
The equation (sin x)^2 – 4 sin x + 4 = 0 has no solutions because it can be rewritten as (sin x - 2)^2 = 0. This implies that sin x - 2 must be zero, so sin x = 2. However, the range of the sine function is [-1, 1], meaning sine values cannot exceed 1 or fall below -1. Since 2 is outside this range, there are no real values of x for which this equation holds true.
equation has no solution because it implies sin x = 2, which is impossible since the sine function has a range of [-1, 1].