Final answer:
The values of x for which the equation tan⁻¹(tan x) = x is true lie between -π/2 and π/2.
Step-by-step explanation:
To find the values of x for which the equation tan⁻¹(tan x) = x is true, we need to understand the properties of the inverse tangent function. The inverse tangent function, tan⁻¹, takes as input the tangent of an angle and returns the angle itself. However, the inverse tangent function has a limited range of values. It is defined for angles between -π/2 and π/2.
Therefore, for the equation to be true, x must lie in the range of values for which tan⁻¹(x) is defined. This means that x must be between -π/2 and π/2.
In summary, the values of x for which the equation tan⁻¹(tan x) = x is true are -π/2 ≤ x ≤ π/2.