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For the function $\tan x$, when $x = \frac\pi2$, the answer is undefined. But when graphing $\cot x$ or $\frac 1{\tan x}$, when $x = \frac\pi2$, the answer is 0 and not undefined. Shouldn't subbing in $\frac\pi2$ for $\frac 1{\tan x}$result in an undefined answer?

Amruth Arunkumar
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    $\displaystyle \cot(\frac{\pi}{2}) = \frac{\cos(\frac{\pi}{2})}{\sin(\frac{\pi}{2})} = \frac{0}{1} = 0$ – Joshua Wang Aug 27 '22 at 21:06
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    $\cot x=\frac1{\tan x}$ is an identity that holds in the intersection of the domains. It shouldn't be read as implying that the functions have the same domain. – Sassatelli Giulio Aug 27 '22 at 21:10

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