Question

нужно упростить это выражение пожалуйста​

Answer 1

$\frac{Cos\alpha-2Sin\alpha}{Sin\alpha+Cos\alpha}-\frac{2-Cos^{2}\alpha}{Cos2\alpha}=\frac{Cos\alpha-2Sin\alpha}{Sin\alpha+Cos\alpha}-\frac{2-Cos^{2}\alpha}{Cos^{2}\alpha-Sin^{2}\alpha}=\\\\=\frac{Cos\alpha-2Sin\alpha}{Sin\alpha+Cos\alpha}-\frac{2-Cos^{2}\alpha}{(Cos\alpha-Sin\alpha)(Cos\alpha+Sin\alpha)}=\frac{(Cos\alpha-2Sin\alpha)(Cos\alpha-Sin\alpha)-2+Cos^{2}\alpha}{(Cos\alpha-Sin\alpha)(Cos\alpha+Sin\alpha)}=$

$=\frac{Cos^{2}\alpha-Sin\alpha Cos\alpha-2Sin\alpha Cos\alpha+2Sin^{2}\alpha-2+Cos^{2}\alpha}{(Cos\alpha-Sin\alpha)(Cos\alpha+Sin\alpha)}=\frac{2(Cos^{2}\alpha+Sin^{2}\alpha)-2-3Sin\alpha Cos\alpha}{Cos2\alpha}=\\\\=-\frac{3Sin\alpha Cos\alpha}{Cos2\alpha}=-\frac{1,5Sin2\alpha }{Cos2\alpha} =\boxed{-1,5tg2\alpha}$