Solve for x 2sin(2x)- square root of 3=0

Problem

2*sin(2*x)−√(,3)=0

Solution

1. Isolate the trigonometric term by adding √(,3) to both sides and then dividing by 2

2*sin(2*x)=√(,3)

sin(2*x)=√(,3)/2

2. Identify the reference angle for which the sine value is √(,3)/2 which is π/3 (or 60.

sin(θ)=√(,3)/2⇒θ=π/3,(2*π)/3

3. Set up the general solution equations for the argument 2*x including the period 2*π*n where n is an integer.

2*x=π/3+2*π*n

2*x=(2*π)/3+2*π*n

4. Solve for x by dividing both sides of each equation by 2

x=π/6+π*n

x=π/3+π*n

Final Answer

x=π/6+π*n,π/3+π*n

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