Solve for x 2cos(2x)-1=0

Problem

2*cos(2*x)−1=0

Solution

1. Isolate the cosine term by adding 1 to both sides and then dividing by 2.

2*cos(2*x)=1

cos(2*x)=1/2

2. Determine the general solutions for the angle 2*x by identifying where the cosine function equals 1/2 on the unit circle.

2*x=π/3+2*π*n

2*x=−π/3+2*π*n

3. Solve for x by dividing all terms in both equations by 2.

x=π/6+π*n

x=−π/6+π*n

Final Answer

x=±π/6+π*n,n∈ℤ

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