Solve for x tan(x)=4

Problem

tan(x)=4

Solution

1. Apply the inverse tangent function to both sides of the equation to isolate x

arctan(tan(x))=arctan(4)

2. Simplify the left side using the property that arctan(tan(x))=x for values within the principal range.

x=arctan(4)

3. Account for the periodicity of the tangent function, which has a period of π

x=arctan(4)+n*π

4. Specify the domain for the integer constant n

n∈ℤ

Final Answer

tan(x)=4⇒x=arctan(4)+n*π,n∈ℤ

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