Trigonometry (10th Edition)

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

Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 195: 61

Answer

$$\sec\theta\cot\theta\sin\theta=1$$

Work Step by Step

$$A=\sec\theta\cot\theta\sin\theta$$ - Quotient Identity: $$\cot\theta=\frac{\cos\theta}{\sin\theta}$$ - Reciprocal Identity: $$\sec\theta=\frac{1}{\cos\theta}$$ We replace these into $A$, and we have $$A=\frac{1}{\cos\theta}\times\frac{\cos\theta}{\sin\theta}\times\sin\theta$$ After all the eliminations, we are left with $$A=1$$
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