Solve for x 2sin(2x)- square root of 2=0

Problem

2*sin(2*x)−√(,2)=0

Solution

1. Isolate the trigonometric term by adding √(,2) to both sides and then dividing by 2

2*sin(2*x)=√(,2)

sin(2*x)=√(,2)/2

2. Identify the reference angles where the sine function equals √(,2)/2 within the first rotation.

sin(θ)=√(,2)/2⇒θ=π/4,(3*π)/4

3. Set the argument 2*x equal to the general solutions for these angles, where n is any integer.

2*x=π/4+2*n*π

2*x=(3*π)/4+2*n*π

4. Solve for x by dividing all terms in both equations by 2

x=π/8+n*π

x=(3*π)/8+n*π

Final Answer

x=π/8+n*π,(3*π)/8+n*π

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