# Answer to this double-angle formulae equation in trigonometry?

## ${\left(C o s \left(\frac{\pi}{12}\right) + S \in \left(\frac{\pi}{12}\right)\right)}^{2}$

${\left(C o s \left(\frac{\pi}{12}\right) + S \in \left(\frac{\pi}{12}\right)\right)}^{2}$
$= C o {s}^{2} \left(\frac{\pi}{12}\right) + S {\in}^{2} \left(\frac{\pi}{12}\right) + 2 \sin \left(\frac{\pi}{12}\right) \cos \left(\frac{\pi}{12}\right)$
$= 1 + \sin \left(2 \times \frac{\pi}{12}\right)$
$= 1 + \sin \left(\frac{\pi}{6}\right)$
$= 1 + \frac{1}{2} = \frac{3}{2}$