It is known that if g and h are two continuous functions, then
It has to be proved first that g (x) = sin x and h (x) = cos x are continuous functions.
Let g (x) = sin x
It is evident that g (x) = sin x is defined for every real number.
Let c be a real number. Put x = c + h
Therefore, g is a continuous function.
Let h (x) = cos x
It is evident that h (x) = cos x is defined for every real number.
Let c be a real number. Put x = c + h If x ® c, then h ® 0 h (c) = cos c
Therefore, h (x) = cos x is continuous function. It can be concluded that,
Therefore, cotangent is continuous except at x = np, n Î Z
