Question

Алгебра.
Задание 321.

Answer 1

$1)\frac{Sin\alpha +Sin3\alpha}{Cos\alpha+Cos3\alpha}=\frac{2Sin\frac{\alpha+3\alpha}{2}Cos\frac{\alpha-3\alpha}{2}}{2Cos\frac{\alpha+3\alpha}{2}Cos\frac{\alpha-3\alpha}{2}}=\frac{Sin2\alpha Cos\alpha}{Cos2\alpha Cos\alpha}=\frac{Sin2\alpha}{Cos2\alpha}=tg2\alpha\\\\\boxed{tg2\alpha=tg2\alpha}$

$2)\frac{Sin2\alpha +Sin4\alpha}{Cos2\alpha-Cos4\alpha}=\frac{2Sin\frac{2\alpha+4\alpha}{2}Cos\frac{2\alpha-4\alpha}{2}}{-2Sin\frac{2\alpha+4\alpha}{2}Sin\frac{2\alpha-4\alpha}{2}}=\frac{Sin3\alpha Cos\alpha}{-Sin3\alpha Sin(-\alpha)}=\frac{Sin3\alpha Cos\alpha}{Sin3\alpha Sin\alpha} =\\\\=\frac{Cos\alpha }{Sin\alpha}=Ctg\alpha\\\\\boxed{Ctg\alpha=Ctg\alpha}$