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

Problem

tan2(x)=1/3

Solution

1. Take the square root of both sides of the equation to isolate the trigonometric function.

tan(x)=±√(,1/3)

2. Simplify the radical by rationalizing the denominator.

tan(x)=±1/√(,3)

tan(x)=±√(,3)/3

3. Identify the reference angle in the first quadrant where the tangent value is √(,3)/3

x=π/6

4. Determine the general solution by considering all quadrants where the tangent is positive or negative and using the period of the tangent function, which is π

x=π/6+n*π

x=−π/6+n*π

5. Combine the solutions into a single expression where n is any integer.

x=±π/6+n*π

Final Answer

tan2(x)=1/3⇒x=π/6+n*π,−π/6+n*π

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