Question

Как упрощается данное выражение?

Answer 1

$\frac{1-2Sin^{2}\alpha}{2tg(45^{o}-\alpha )*Cos^{2}(45^{o}-\alpha} =\frac{Cos2\alpha }{\frac{2Sin(45^{o}-\alpha)}{Cos(45^{o}-\alpha)}*Cos^{2}(45^{o}-\alpha)}= \frac{Cos2\alpha }{2Sin(45^{o}-\alpha)Cos(45^{o}-\alpha)} =\frac{Cos2\alpha }{Sin(90^{o}-2\alpha)}=\frac{Cos2\alpha }{Cos2\alpha }=1$