How do you find the limit of ##x/sinx## as x approaches 0?

##1##

Let ##f(x)=x/sinx##

##implies f'(x)=lim_(x to 0) x/sinx##

##implies f'(x)=lim_(x to 0) 1/(sinx/x)=(lim_(x to 0)1)/(lim_(x to 0)(sinx/x))=1/1=1##

NOTE The question was posted in "Determining Limits Algebraically" , so the use of L'Hôpital's rule is NOT a suitable method to solve the problem