Show that sec x is a continuous function.

Question

Philoid · Accepted Answer

Let f(x) = sec x

Therefore, f(x) =

f(x) is not defined when cos x = 0

And cos x = 0 when, x = and odd multiples of like

Let us consider the function

f(a) = cos a and let c be any real number. Then,

= cos c - sin c

= cos c (1) – sin c (0)

Therefore,

cos c

Similarly,

f(c) = cos c

Therefore,

f(c) = cos c

So, f(a) is continuous at a = c

Similarly, cos x is also continuous everywhere

Therefore, sec x is continuous on the open interval