Solve for x 4cos(4x)^2-3=0

Problem

4*cos2(4*x)−3=0

Solution

1. Isolate the squared trigonometric term by adding 3 to both sides and then dividing by 4

cos2(4*x)=3/4

2. Take the square root of both sides, remembering to include both the positive and negative roots.

cos(4*x)=±√(,3)/2

3. Identify the reference angle for which the cosine is √(,3)/2 which is π/6

cos(θ)=±√(,3)/2⇒θ=π/6+n*π* or *θ=(5*π)/6+n*π

4. Combine these solutions into a single general expression for the angle 4*x

4*x=π/6+(n*π)/2

5. Solve for x by dividing the entire expression by 4

x=π/24+(n*π)/8

Final Answer

x=π/24+(n*π)/8

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