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For what values of x is the equation tan⁻¹ (tan x)=x true?

User Wisperwind
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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.

User Bronson
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