Question

$\cos(a) + 1 = 2 {cos}^{2} \frac{a}{2}$
prove that

Answer 1

$\cos( \alpha ) = \cos( \frac{ \alpha }{2} + \frac{ \alpha }{2} ) \\ \cos( \alpha ) = \cos {}^{2} ( \frac { \alpha }{2} ) - \sin {}^{2} ( \frac{ \alpha }{2} ) \\ \cos( \alpha ) = 2 \cos {}^{2} ( \frac{ \alpha }{2} ) - 1 \\ \cos( \alpha ) + 1 = 2 \cos {}^{2} ( \frac{ \alpha }{2} )$