True or False? The statement tan(tan-1(x)) = x, for all real numbers in the interval −(𝜋)/2 < x < 𝜋/2 .

Answer 1

This is true for -∞ < x < ∞.

Answer 2

The above statement is true by the definition of the arctan function. The tangent function is bijective on (-pi/2 , pi/2) and its inverse is the arctan on this interval.

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