Find all solutions to the following equation:

sin^2 (x) cos^2 (x) = 1/4

We are given the equation sin^2 (x) cos^2 (x) = 1/4 and is asked to evaluate the x-value of the equation given. we first start by taking the square root of both sides resulting to sin (x) cos (x) = 1/2. By double angle identity, 1/2 sin 2x = 1/2. Simplifying, sin 2x = 1; x is equal to pi/4.

sin² (x) cos² (x) = ¹/₄

√sin² (x) cos² (x) = √¹/₄

sin (x) cos (x) = ¹/₂

2sin (x) cos (x) = 1

sin (2x) = 1

sin⁻¹[sin (2x) ] = sin⁻¹ (1)

2x = 90

2 2

x = 45