Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 6 - Analytic Trigonometry - Section 6.5 Sum and Difference Formulas - 6.5 Assess Your Understanding - Page 509: 47


See proof below.

Work Step by Step

Apply the sum formula: $\sin(A+B)=\sin(A)\cos(B)+\cos(A)\sin(B)$ In order to prove the given identity, we simplify the left-hand side $\text{LHS}$ as follows: $\text{LHS } =\sin(\dfrac{\pi}{2}+\theta) \\=\sin(\dfrac{\pi}{2})\cos(\theta)+\sin(\theta)\cos(\dfrac{\pi}{2}) \\=1\cdot \cos(\theta)+0\cdot \sin(\theta) \\=\cos(\theta)+0 \\=\cos{\theta} \\=\text{ RHS}$
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