Question

Is $\cot$ the same as $\tan$ inverse of $1?$

Answer 1

Determining if $cot$ is the same as $\tan$ inverse of $1$

$Co\tan gent$ function is the reciprocal of $\tan gent$ function

i.e. $\cot \left(x\right)=\frac{1}{\tan \left(x\right)}$

While, inverse of $\tan gent$ function is denoted as ${\tan }^{-1}\left(x\right)$

From this, we can say if, $y=\tan \left(x\right),\mathrm{then}x={\tan }^{-1}\left(y\right)$.

Therefore, $cot\left(x\right)$ is not same as ${\tan }^{-1}\left(x\right)$.