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 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 219: 60


The given statement $$\cos140^\circ=\cos60^\circ\cos80^\circ-\sin60^\circ\sin80^\circ$$ is true.

Work Step by Step

$$\cos140^\circ=\cos60^\circ\cos80^\circ-\sin60^\circ\sin80^\circ$$ As $140^\circ=60^\circ+80^\circ$, $$\cos140^\circ=\cos(60^\circ+80^\circ)$$ Now we use the cosine sum identity $$\cos(A+B)=\cos A\cos B-\sin A\sin B$$ (be extremely careful about the sign in the middle) to expand $\cos(60^\circ+80^\circ)$: $$\cos140^\circ=\cos60^\circ\cos80^\circ-\sin60^\circ\sin80^\circ$$ This means that the statement $$\cos140^\circ=\cos60^\circ\cos80^\circ-\sin60^\circ\sin80^\circ$$ is true.
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