Question

1-2sin^2a= (2cos^2a * tga)/tg2a

Answer 1

$1-2 sin^{2} alpha =cos2 alpha =frac{ 2cos^{2} alpha *tg alpha }{tg2 alpha }$ 
$1- 2sin^{2} alpha =cos2 alpha$
$cos2 alpha = 2cos ^{2} alpha *frac{sin alpha *cos2 alpha }{cos alpha *sin2 alpha }$
$cos2 alpha = frac{ 2cos^{2} alpha *sin alpha *cos2 alpha }{2 cos^{2} alpha *sin alpha }$
$cos2 alpha =cos 2alpha$