Solve for x 4cos(x)^2=1

Problem

4*cos2(x)=1

Solution

1. Isolate the squared trigonometric term by dividing both sides of the equation by 4

cos2(x)=1/4

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

cos(x)=±√(,1/4)

cos(x)=±1/2

3. Solve for x by identifying the angles on the unit circle where the cosine value is 1/2 or −1/2

x=π/3+n*π

x=(2*π)/3+n*π

4. Combine the solutions into a single general expression where n is any integer.

x=π/3+n*π,(2*π)/3+n*π

Final Answer

x=π/3+n*π,(2*π)/3+n*π

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