Solve for x tan(x)^2=3

Problem

tan2(x)=3

Solution

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

tan(x)=±√(,3)

2. Identify the reference angle for which the tangent function equals √(,3)

tan(π/3)=√(,3)

3. Determine the general solution for x by considering the periodicity of the tangent function, which is π

x=π/3+n*π

x=−π/3+n*π

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

x=±π/3+n*π

Final Answer

tan2(x)=3⇒x=π/3+n*π,−π/3+n*π

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