Solve for x square root of 3tan(x)-1=0

Problem

√(,3)*tan(x)−1=0

Solution

1. Isolate the term containing the tangent function by adding 1 to both sides of the equation.

√(,3)*tan(x)=1

2. Divide both sides by √(,3) to solve for tan(x)

tan(x)=1/√(,3)

3. Rationalize the denominator (optional but helpful) to recognize the standard value from the unit circle.

tan(x)=√(,3)/3

4. Identify the reference angle where the tangent is √(,3)/3 which occurs at x=π/6 (or 30.

x=π/6

5. Determine the general solution by adding the period of the tangent function, which is n*π for any integer n

x=π/6+n*π

Final Answer

√(,3)*tan(x)−1=0⇒x=π/6+n*π

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