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 solution for the angle 2*x by finding where the cosine function equals 1/2 on the unit circle.

2*x=π/3+2*k*π

2*x=−π/3+2*k*π

3. Solve for x by dividing the entire expression by 2, where k is any integer.

x=π/6+k*π

x=−π/6+k*π

Final Answer

x=±π/6+k*π,k∈ℤ

Want more problems? Check here!