Question

Find all solutions to the equation
sin^2(x)cos^2(x) = (2 - √2) / 16

Answer 1

1/2(1 - cos(2x))*1/2(1 + cos(2x)) = (2 - √2) / 16
1/4(1 - cos^2(2x)) = (2 - √2) / 16
1/4(1 - 1/2(1 + cos(4x)) = (2 - √2) / 16
1/8(2 - 1 - cos(4x)) = (2 - √2) / 16
1/8(1 - cos(4x)) = (2 - √2) / 16
1 - cos(4x) = (2 - √2) / 2 = 1 - √2/2
cos(4x) = √2/2
4x = arccos(√2/2) = π/4
x = π/16

The solutions are: nπ - 15π/16, nπ - 9π/16, nπ - 7π/16, nπ - π/16.