Question

Simplify $\sqrt{2+\sqrt{2+2\cos (\pi +{60}^0)}}$

Answer 1

$\sqrt{2+\sqrt{2+2\cos (\pi +{60}^0)}}$
$=\sqrt{2+\sqrt{2-2\cos {60}^0}}$
$(because\cos (\pi +\theta )=-\cos \theta )$
$=\sqrt{2+\sqrt{2-2\times \frac{1}{2}}}$
$=\sqrt{2+\sqrt{1}}=\sqrt{3}$