You are supposed to use the identity for the sine of a sum of angles and the theorems about the limit of the sum and product of functions.
to prove that sine is continuous we need to show that lim_{x-->} 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
lim_{h-->0}sin(a+h) = sin(a)
use the theorem:
lim_{x-->0}cos(x) = 1 and lim_{x-->0}sin(x)=0
to show that this is true.
please help me with detailed steps!
You are supposed to use the identity for the sine of a sum of angles and the theorems about the limit of the sum and product of functions.