   Chapter 2.R, Problem 58E

Chapter
Section
Textbook Problem

# (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.

To determine

(a)

To obtain:

Double angle formula for sine function.

Explanation

1) Formula:

i. Sum rule:

ddxfx+gx=ddxfx+ddxg(x)

ii. Difference rule:

ddxfx-gx=ddxfx-ddxg(x)

iii. Power rule combined with chain rule:

ddxfxn=n.fxn-1.f'(x)

iv. ddxcosf(x)=-sinfx.f'(x)

v. ddxsinf(x)=cosfx.f'(x)

2) Given:

cos2x=cos2x-sin2x

3) Calculation:

cos2x<

To determine

(b)

To obtain:

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