Solve for x cos(2x)=( square root of 3)/2

Problem

cos(2*x)=√(,3)/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 of arccos(√(,3)/2) Since cos(π/6)=√(,3)/2 the reference angle is π/6

3. Set up the equation for the argument 2*x using the general solution form.

2*x=2*n*π±π/6

4. Isolate x by dividing the entire equation by 2

x=(2*n*π±π/6)/2

5. Simplify the expression to find the final general solution for x

x=n*π±π/12

Final Answer

cos(2*x)=√(,3)/2⇒x=n*π±π/12

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