Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 5 - Section 5.5 - Additional Identities - 5.5 Problem Set - Page 312: 36

Answer

See below.

Work Step by Step

We must verify $\cos A-\cos B=-2\sin\frac{A+B}{2}\sin\frac{A-B}{2}$ with $A=90,B=30$, plugging in these we get: $\cos 90-\cos 30=-2\sin\frac{90+30}{2}\sin\frac{90-30}{2}\\0-\sqrt3/2=-2\sin60\sin(30)\\-\sqrt3/2=-2(\sqrt3/2)(0.5)$ This is true, hence we verified what we had to.
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