Solve for x tan(x)^2-1/3=0

Problem

tan(x)−1/3=0

Solution

1. Isolate the squared trigonometric term by adding 1/3 to both sides of the equation.

tan(x)=1/3

2. Take the square root of both sides, remembering to include both the positive and negative roots.

tan(x)=±√(,1/3)

3. Simplify the radical expression on the right side.

tan(x)=±1/√(,3)

4. Identify the reference angle in the first quadrant where the tangent function equals 1/√(,3)

x=π/6

5. Determine the general solution by considering the period of the tangent function, which is π

x=π/6+n*π

x=−π/6+n*π

6. Combine the solutions into a single expression using the symmetry of the tangent function.

x=π/6+n*π

x=(5*π)/6+n*π

Final Answer

tan(x)−1/3=0⇒x=π/6+n*π,(5*π)/6+n*π

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