Question

упростите выражения
(и мою жизнь)​

Answer 1

$1)\frac{Sin2\alpha}{Sin\alpha}=\frac{2Sin\alpha Cos\alpha}{Sin\alpha}=2Cos\alpha$

$2)\frac{Sin2\alpha}{Cos^{2}\alpha-Sin^{2}\alpha}=\frac{Sin2\alpha}{Cos2\alpha}=tg2\alpha$

$3)Cos2\alpha+Sin^{2} \alpha=Cos^{2}\alpha-Sin^{2}\alpha+Sin^{2}\alpha=Cos^{2}\alpha$

$4)\frac{Sin50^{0}}{2Cos25^{0}}=\frac{2Sin25^{0}Cos25^{0}}{2Cos25^{0}}=Sin25^{0}$

$5)\frac{Cos2\alpha}{Cos\alpha-Sin\alpha}=\frac{Cos^{2}\alpha-Sin^{2}\alpha}{Cos\alpha-Sin\alpha}=\frac{(Cos\alpha-Sin\alpha)(Cos\alpha+Sin\alpha)}{Cos\alpha-Sin\alpha}=Cos\alpha+Sin\alpha$

$6)1-2Sin^{2}\frac{\alpha}{4} = Cos(2*\frac{\alpha}{4})=Cos\frac{\alpha}{2}$