Solve for x cos(2x)=1/2

Problem

cos(2*x)=1/2

Solution

1. Identify the general solution for the cosine function. For an equation cos(θ)=a the solution is θ=2*n*π±arccos(a) where n is an integer.

2. Determine the principal value. Since cos(π/3)=1/2 we have arccos(1/2)=π/3

3. Set up the equation for the argument 2*x

2*x=2*n*π±π/3

4. Isolate x by dividing the entire expression by 2

x=n*π±π/6

Final Answer

cos(2*x)=1/2⇒x=n*π±π/6

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