1. 4 cos²(2x) - 3 = 0
cos²(2x) = 3/4
cos(2x) = ± √(3/4) = ±√3/2
Remember, cos(Θ) = ±√3/2 when Θ = 30°, 150°
So, 2x = 30° and 2x = 150°
x = 15° and x = 75°
both meet the criterion 0 ≤ x ≤ 90
2. ...
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1. 4 cos²(2x) - 3 = 0
cos²(2x) = 3/4
cos(2x) = ± √(3/4) = ±√3/2
Remember, cos(Θ) = ±√3/2 when Θ = 30°, 150°
So, 2x = 30° and 2x = 150°
x = 15° and x = 75°
both meet the criterion 0 ≤ x ≤ 90
2. 2 sin²(x) - sin(x) = 0
sin(x) * (2 sin(x) - 1) = 0
So either sin(x) = 0 or 2sin(x) - 1 = 0
sin(x) = 0 when x = 0° or 180°
2sin(x) - 1 = 0 --> sin(x) =1/2
sin(x) = 1/2 when x = 30° or x = 150°
To satisfy the criterion 0 ≤ x ≤ 90,
x = 0° or 30°