#### Answer

No, $\tan^{-1}$x is not the reciprocal of $\tan x.$
(It is the inverse of tan)

#### Work Step by Step

Entering $\tan^{-1}25^{o}$, the calculator returns
87.7093899574,
which is the angle (in degrees) for which tan is 25.
To check, enter $\tan($87.7093899574$)$.... result=25.
To get $\cot 25^{o}$, he should have entered
$(\tan 25)^{-1}$ or $1/\tan 25$
with the result : 2.14450692051
$\tan^{-1}$x is not the reciprocal of $\tan x.$
(It is the inverse of tan)