Solve for x 9tan(x)^2-3=0

Problem

9*tan(x)−3=0

Solution

1. Isolate the squared trigonometric term by adding 3 to both sides and then dividing by 9

9*tan(x)=3

tan(x)=3/9

tan(x)=1/3

2. Take the square root of both sides to solve for tan(x) remembering to include both the positive and negative roots.

tan(x)=±√(,1/3)

tan(x)=±1/√(,3)

3. Rationalize the denominator to identify the standard values from the unit circle.

tan(x)=±√(,3)/3

4. Identify the angles x within one period (−π/2,π/2) that satisfy the equation.

x=π/6

x=−π/6

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

x=π/6+n*π

x=−π/6+n*π

Final Answer

x=±π/6+n*π

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