Question -
Answer -
It isknown that if g and h are two continuousfunctions, then
Ithas to be proved first that g (x) = sin x and h (x)= cos x are continuous functions.
Let g (x)= sin x
It isevident that g (x) = sin x is definedfor every real number.
Let c bea real number. Put x = c + h
If x
c, then h
0
Therefore, g isa continuous function.
Let h (x)= cos x
It isevident that h (x) = cos x is definedfor every real number.
Let c bea 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 concludedthat,
Therefore, cosecant is continuous except at x = np, n Z
Therefore, secant is continuous except at 
Therefore,cotangent is continuous except at x = np, n Î Z