determine all the values of x?

Question

determine all of the values of x such that
sin^5x + cos^5x = 1 and 0 ≤ x ≤ π/2

Answer 1

Well, 0 and 90 degrees obviously works.

Since (Sin(x))^2 + (Cos(x))^2 = 1, then (Sin(x))^5 + (Cos(x))^5 < 1 between 0 and π/2, so that 0 and π/2 would be the only two solutions.