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 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 208: 42



Work Step by Step

$$A=\frac{1}{\tan^2\alpha}+\cot\alpha\tan\alpha$$ $$A=\Big(\frac{1}{\tan\alpha}\Big)^2+\cot\alpha\tan\alpha$$ According to a Reciprocal Identity: $$\cot\alpha=\frac{1}{\tan\alpha}$$ so, $$\Big(\frac{1}{\tan\alpha}\Big)^2=\cot^2\alpha\hspace{1cm}(1)$$ Also, we can deduce that $$\cot\alpha\tan\alpha=1\hspace{1cm}(2)$$ Combine $(1)$ and $(2)$ into $A$: $$A=\cot^2\alpha+1$$ $$A=\csc^2\alpha\hspace{1cm}\text{(Pythagorean Identity)}$$
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