Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Section 1.3 - Trigonometric Functions - Exercises 1.3 - Page 28: 35

Answer

$\cos{(A-B)} = \cos{A} \cos{B} + \sin{A} \sin{B} = \text{ RHS}$

Work Step by Step

Addition formula $$\cos{(A+B)}= \cos{A} \cos{B}-\sin{A}\sin{B}$$ $\therefore \cos{(A-B)} = \cos{A} \cos{(-B)} - \sin{A} \sin{(-B)}$ $\cos{(A-B)} = \cos{A} \cos{B} - \sin{A} (-\sin{B})$ $\cos{(A-B)} = \cos{A} \cos{B} + \sin{A} \sin{B} = \text{ RHS}$
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