Discuss the continuity of the cosine, cosecant, secant and cotangent functions.

Explanation

(i) Let `f(x) = cos x`
If a `ne` R then at x = a
`underset(x to a)(lim)f(x) = underset (x to a)(lim)cos x = cos a = f(a)`
`:. F(x)` is contiuous at x = a
but a is an arbitrary point.
`:. f(x)` is continuous at every point.
(ii) `:'` cosec x is not contnuous at x = n `pi`, n `in` Z.
`:. cosec x` is not continuous at x = n`pi`, n `in` Z.
(iii) `:'` sec x is not defined atx = (2n + 1) .(`pi`)/(2), n `in` Z.
`:.` sec x is not continuous atx = (2x + 1 ).(`pi`)/(2), n `in` Z.
(iv) `:'` cot x is not defined at x = n`pi` , n `in` Z.
`:.` cot x is not continous at x = n `pi` , n `in` Z.