Question

Помогите плиз, даю много баллов!!​

Answer 1

$1)\frac{Cos6\alpha }{Sin2\alpha } +\frac{Sin6\alpha }{Cos2\alpha }=\frac{Cos6\alpha Cos2\alpha +Sin6\alpha Sin2\alpha}{Sin2\alpha Cos2\alpha}=\frac{Cos(6\alpha -2\alpha)}{Sin2\alpha Cos2\alpha}=\frac{Cos4\alpha }{Sin2\alpha Cos2\alpha}=\frac{2Cos4\alpha }{2Sin2\alpha Cos2\alpha} =\frac{2Cos4\alpha}{Sin4\alpha }=2Ctg4\alpha=2*\frac{1}{tg4\alpha }=\frac{2}{tg4\alpha }$

$\frac{2}{tg4\alpha}=\frac{2}{tg4\alpha }$

Тождество доказано

$2)\frac{tg\alpha }{1+tg\alpha }+\frac{tg\alpha }{1-tg\alpha }=\frac{tg\alpha-tg^{2}\alpha+tg\alpha+tg^{2}\alpha}{(1+tg\alpha)(1-tg\alpha)}=\frac{2tg\alpha }{1-tg^{2}\alpha}=tg2\alpha\\\\tg2\alpha=tg2\alpha$

Тождество доказано