Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.5 Double-Angle Identities - 5.5 Exercises - Page 237: 58



Work Step by Step

$$A=2\cos85^\circ\sin140^\circ$$ The product-to-sum identity that will be applied here is $$\cos X\sin Y=\frac{1}{2}[\sin(X+Y)-\sin(X-Y)]$$ Therefore, A would be $$A=2\times\frac{1}{2}[\sin(85^\circ+140^\circ)-\sin(85^\circ-140^\circ)]$$ $$A=\sin225^\circ-\sin(-55^\circ)$$ We know that $\sin(-X)=-\sin X$. That means $$A=\sin225^\circ+\sin55^\circ$$
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