What is the Value of Cot 90 Degrees ?

Solution :

The value of cot 90 degrees is 0.

Proof :

$\angle$ A of $\Delta$ ABC is made large and large until it becomes 90 degrees. As $\angle$ A gets large and large $\angle$ C gets smaller and smaller. Side AB goes on decreasing. The point A gets closer to point B. When $\angle$ C becomes very close to 0 degree. The side AC almost coincide with side BC and side AB becomes to zero.

So, AC = BC and AB = 0

By using trigonometric formulas,

$cot 90^{\circ}$ = $base\over perpendicular$ = $b\over p$

$cot 90^{\circ}$ = $AB\over BC$ = $0\over BC$ = 0

Hence, the value of $cot 90^{\circ}$ = 0.