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

Problem

cos(2*x)=√(,2)/2

Solution

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

2. Determine the principal value. We know that cos(π/4)=√(,2)/2

3. Set up the equations for the argument 2*x based on the general solution.

2*x=2*π*n±π/4

4. Isolate x by dividing the entire expression by 2

x=π*n±π/8

Final Answer

cos(2*x)=√(,2)/2⇒x=π*n±π/8

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