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.

 

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