The statement tan(tan $\tan \left( \tan ^ { - 1 } x \right) = x$ x for all real numbers in the interval
-$- \frac { \pi } { 2 }

Name: The statement tan(tan $\tan \left( \tan ^ { - 1 } x \right) = x$ x for all real numbers in the interval -$- \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$
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Question

The statement tan(tan $\tan \left( \tan ^ { - 1 } x \right) = x$ x for all real numbers in the interval
-$- \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$

Quizplus · Accepted Answer

For all real numbers $x$ in the interval $-\frac{\pi}{2} < x < \frac{\pi}{2}$, $\tan^{-1}x$ will give an angle whose tangent is $x$, thus applying the tangent function again will return to the original value $x$.

The Statement Tan(tan tan⁡(tan⁡−1x)=x\tan \left( \tan ^ { - 1 } x \right) = xtan(tan−1x)=x

The Statement Tan(tan $\tan \left( \tan ^ { - 1 } x \right) = x$