Chapter 2.5, Problem 66E

To prove that sine is continuous, we need to show that ${\underset{}{\lim }}_{x\to a}\sin x=\sin a$ for every real number a. By Exercise 63 an equivalent statement is that

$\underset{h\to 0}{\lim }\sin (a+h)=\sin a$

Use (6) to show that. this is true.