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=±arccos(a)+2*π*k where k is any 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.

θ=2*x

2*x=π/4+2*π*k

2*x=−π/4+2*π*k

4. Isolate x by dividing both sides of each equation by 2

x=π/8+π*k

x=−π/8+π*k

Final Answer

cos(2*x)=√(,2)/2⇒x=±π/8+π*k

Want more problems? Check here!