## Trigonometry (10th Edition)

Published by Pearson

# Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises: 56

True

#### Work Step by Step

$\cos$ 60$^{\circ}$ = 2 $\cos$$^{2} 30^{\circ} - 1 \cos 60^{\circ} = \frac{1}{2} \cos 30^{\circ} = \frac{\sqrt3}{2} 2 \cos$$^{2}$ 30$^{\circ}$ - 1 = 2($\frac{\sqrt3}{2}$)$^{2}$ - 1 2 $\cos$$^{2} 30^{\circ} - 1 = 2(\frac{3}{4}) - 1 2 \cos$$^{2}$ 30$^{\circ}$ - 1 = ($\frac{6}{4}$) - 1 2 $\cos$$^{2} 30^{\circ} - 1 = (\frac{3}{2}) - 1 2 \cos$$^{2}$ 30$^{\circ}$ - 1 = ($\frac{1}{2}$) Thus: $\frac{1}{2}$ = $\frac{1}{2}$ Therefore, $\cos$ 60$^{\circ}$ = 2 $\cos$$^{2}$ 30$^{\circ}$ - 1 is a true statement.

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