to prove that sine is continuous we need to show that limx--> sin(x)=sin(a) for every real number a. if we let h=x-a, then x=a+h and x-->a <--> h-->0. so an equivalent statement is that
limh-->0sin(a+h) = sin(a)
use the theorem:
limx-->0cos(x) = 1 and limx-->0sin(x)=0
to show that this is true.
please help me with detailed steps!