Question

Find all solutions to the following equation:

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

Answer 1

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

Answer 2

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.