Question

635. упростите выражение​

Answer 1

$\displaystyle\bf\\\frac{Sin\alpha -Cos\alpha }{1-2Cos^{2} \alpha } =\frac{Sin\alpha -Cos\alpha }{Sin^{2}\alpha +Cos^{2}\alpha -2Cos^{2} \alpha}=\frac{Sin\alpha -Cos\alpha }{Sin^{2}\alpha -Cos^{2} \alpha} =\\\\\\=\frac{Sin\alpha -Cos\alpha }{(Sin\alpha -Cos\alpha )(Sin\alpha +Cos\alpha )} =\frac{1}{Sin\alpha +Cos\alpha }$