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

Problem

4*cos(x)=1+2*cos(x)

Solution

1. Subtract 2*cos(x) from both sides of the equation to group the trigonometric terms.

4*cos(x)−2*cos(x)=1

2. Combine the like terms on the left side.

2*cos(x)=1

3. Isolate the cosine function by dividing both sides by 2

cos(x)=1/2

4. Determine the general solution for x by identifying the angles where the cosine value is 1/2

x=±π/3+2*n*π

Final Answer

x=±π/3+2*n*π,n∈ℤ

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