## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 219: 37

#### Answer

$$\theta=15^\circ$$ satisfies what has been given.

#### Work Step by Step

$$\tan\theta=\cot(45^\circ+2\theta)$$ From the identity of the cofunction, we have $$\tan\theta=\cot(90^\circ-\theta)$$ Therefore, compared with what we have been given, we can deduce that $$\cot(45^\circ+2\theta)=\cot(90^\circ-\theta)$$ $$45^\circ+2\theta=90^\circ-\theta$$ $$3\theta=45^\circ$$ $$\theta=15^\circ$$

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