Continuity of sin x and cos xa. Use the identity sin (a + h) = sin a cos h + cos a sin h w...

Continuity of sin x and cos x

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 (a + h) = cos a cos h − sin a sin h with the fact that  to prove that .