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: 33


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

Work Step by Step

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