# How do you verify 1 + cos 2a = 2/(1+ tan^2a)?

$= 1 + \cos 2 \alpha$
$= 1 + \frac{1 - {\tan}^{2} \alpha}{1 + {\tan}^{2} \alpha}$
$= \frac{1 + {\cancel{\tan}}^{2} \alpha + 1 - {\cancel{\tan}}^{2} \alpha}{1 + {\tan}^{2} \alpha}$
$= \frac{2}{1 + {\tan}^{2} \alpha}$=RHS