Q. 44.2( 5 Votes )

Show that sec x is a continuous function.

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


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