a. Use the identity sin (a + h) = sin a cos h + cos a sin h with the fact that to prove that thereby establishing that sin x is continuous for all x. (Hint: Let h = x - a so that x = a + h and note that h→ 0 as x→ a.)

b. Use the identity cos 1a + h2 = cos a cos h - sin a sin h with the fact that to prove that

lim sin x = 0 sin a, lim sin x