## Trigonometry 7th Edition

$\sqrt 2$
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 $\sqrt 2 \times \sqrt 2$) =$\sqrt 2$