Solve for x tan(x)=5

Problem

tan(x)=5

Solution

1. Identify the equation as a basic trigonometric equation where the tangent of an angle x is equal to a constant.

2. Apply the inverse tangent function to both sides of the equation to isolate x for the principal value.

x=arctan(5)

3. Account for the period of the tangent function, which is π to find the general solution.

x=arctan(5)+n*π

4. Define the variable n as any integer to represent all possible solutions.

n∈ℤ

Final Answer

tan(x)=5⇒x=arctan(5)+n*π,n∈ℤ

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