Solve for x, 0°≤x≤90° 1. 4 cos^2 2x-3=0 2. 2 sin^2 x - sin x = 0

Expert Answers

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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°

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