Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 212: 34

Answer

$\tan$ is to be filled in the blank.

Work Step by Step

$$A72^\circ=\cot18^\circ\hspace{1cm}(1)$$ We notice that $$72^\circ+18^\circ=90^\circ$$ That means we can rewrite $(1)$ as $$A72^\circ=\cot(90-72^\circ)\hspace{1cm}(1)$$ Now from the Cofunction Identity: $$\tan\theta=\cot(90^\circ-\theta)$$ So $$A=\tan$$ In other words, we fill in the blank with $\tan$.
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