## Trigonometry (10th Edition)

Published by Pearson

# Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises: 38

#### Answer

$\theta$ = 15$^{\circ}$

#### Work Step by Step

$\cos$(2$\theta$ + 50$^{\circ}$) = $\sin$(2$\theta$ - 20$^{\circ}$) $\cos$ and $\sin$ are cofunctions if the sum of the angles is 90$^{\circ}$ Therefore: (2$\theta$ + 50$^{\circ}$) + (2$\theta$ - 20$^{\circ}$) = 90$^{\circ}$ 4$\theta$ + 30$^{\circ}$ = 90$^{\circ}$ 4$\theta$ = 60$^{\circ}$ $\theta$ = 15$^{\circ}$

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