Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 2 - Section 2.1 - Definition II: Right Triangle Trigonometry - 2.1 Problem Set: 51

Answer

$ \sqrt 2$

Work Step by Step

Given expression = 2 $\cos( 3x - 45^{\circ})$ = 2 $\cos(90^{\circ} - 45^{\circ})$ ( replacing $ x$ with $30^{\circ}$) = 2 $\cos 45^{\circ}$ = 2 $\times (\frac{1}{\sqrt 2})$ ( substituting exact value of $\cos 45^{\circ}$) = $\sqrt 2 \times \sqrt 2 \times (\frac{1}{\sqrt 2})$ (factorising 2 as $\sqrt 2 \times \sqrt 2 $) =$ \sqrt 2$
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