Solve for x tan(x)=2

Problem

tan(x)=2

Solution

1. Identify the equation as a basic trigonometric equation of the form tan(x)=k

2. Apply the inverse tangent function to find the principal value of x in the interval (−π/2,π/2)

x=arctan(2)

3. Determine the general solution by accounting for the periodicity of the tangent function, which has a period of π

x=arctan(2)+n*π

4. Specify the domain for the integer constant n to complete the general solution.

n∈ℤ

Final Answer

tan(x)=2⇒x=arctan(2)+n*π,n∈ℤ

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