#### Problem 58E

58. (a) By differentiating the double-angle formula

$$\cos 2 x=\cos ^{2} x-\sin ^{2} x$$

obtain the double-angle formula for the sine function.

(b) By differentiating the addition formula

$$\sin (x+a)=\sin x \cos a+\cos x \sin a$$

obtain the addition formula for the cosine function.