# How do you verify  1 + tanxtan2x = sec2x?

$\frac{1 + \sin x . \sin 2 x}{\cos x . \cos 2 x} =$
$= \frac{\cos x . \cos 2 x + \sin x . \sin 2 x}{\cos x . \cos 2 x} =$
$= \cos \frac{2 x - x}{\cos x . \cos 2 x} = \frac{1}{\cos} \left(2 x\right)$ = sec 2x