What is the Value of Sec 90 Degrees ?

Solution :

The value of sec 90 degrees is $\infty$ or not defined.

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,

$sec 90^{\circ}$ = $hypotenuse\over base$ = $h\over b$

$sec 90^{\circ}$ = $AC\over AB$ = $AC\over 0$ = $\infty$ or not defined

Hence, the value of $sec 90^{\circ}$ = $\infty$ or not defined.