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

Problem

2*cos2(x)−cos(x)=0

Solution

1. Factor out the common term cos(x) from the left side of the equation.

cos(x)*(2*cos(x)−1)=0

2. Apply the zero product property by setting each factor equal to zero.

cos(x)=0

2*cos(x)−1=0

3. Solve the first equation for x by identifying where the cosine function equals zero.

x=π/2+n*π

4. Isolate the trigonometric term in the second equation.

2*cos(x)=1

cos(x)=1/2

5. Solve the second equation for x by identifying where the cosine function equals 1/2

x=π/3+2*n*π

x=−π/3+2*n*π

Final Answer

x=π/2+n*π,π/3+2*n*π,−π/3+2*n*π

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