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$
