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

[latex]1-2 sin^{2} \alpha =cos2 \alpha =\frac{ 2cos^{2} \alpha *tg \alpha }{tg2 \alpha }[/latex]  [latex]1- 2sin^{2} \alpha =cos2 \alpha [/latex] [latex]cos2 \alpha = 2cos ^{2} \alpha *\frac{sin \alpha *cos2 \alpha }{cos \alpha *sin2 \alpha } [/latex] [latex]cos2 \alpha = \frac{ 2cos^{2} \alpha *sin \alpha *cos2 \alpha }{2 cos^{2} \alpha *sin \alpha } [/latex] [latex]cos2 \alpha =cos 2\alpha [/latex]