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

90 degrees

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.

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