Solve for x tan(3x) = square root of 3

Problem

tan(3*x)=√(,3)

Solution

1. Identify the general solution for the tangent function. The equation tan(θ)=a has solutions θ=arctan(a)+n*π where n is any integer.

2. Determine the principal value. We know that tan(π/3)=√(,3)

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

θ=π/3+n*π

4. Substitute 3*x for θ to solve for x

3*x=π/3+n*π

5. Isolate x by dividing both sides of the equation by 3

x=π/9+(n*π)/3

Final Answer

tan(3*x)=√(,3)⇒x=π/9+(n*π)/3

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