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: 32

Answer

$\cos{\left(x-\dfrac{\pi}{2} \right)} = -\sin{x}= \text{ RHS}$

Work Step by Step

Addition formula $$\cos{(A+B)}= \cos{A} \cos{B}-\sin{A}\sin{B}$$ $\therefore \cos{\left(x+\dfrac{\pi}{2} \right)} = \cos{x} \cos{\left(\dfrac{\pi}{2}\right)} - \sin{x} \sin{\left(\dfrac{\pi}{2} \right)}$ $\cos{\left(x-\dfrac{\pi}{2} \right)} = \cos{x} \times 0 - \sin{x} \times (1) $ $\cos{\left(x-\dfrac{\pi}{2} \right)} = -\sin{x}= \text{ RHS}$
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