Solve for x tan(x)=1

Problem

tan(x)=1

Solution

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

2. Determine the principal value by finding the angle in the interval (−π/2,π/2) whose tangent is 1

3. Recall the unit circle or special triangles, noting that tan(π/4)=1

4. Apply the general solution formula for the tangent function, which is x=arctan(a)+n*π for any integer n

5. Substitute the principal value into the general formula to account for the periodicity of the tangent function, which is π

Final Answer

tan(x)=1⇒x=π/4+n*π,n∈ℤ

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