Question

Упроститк выражение. Прошу помочь с данными примерами!

Answer 1

$1)1+2tg3\alpha*Ctg(\pi-3\alpha)+Sin^{2}\frac{2\alpha}{3} *Ctg^{2}\frac{2\alpha}{3}+Sin^{2} \frac{2\alpha}{3}=\\\\=1+2tg3\alpha*(-Ctg3\alpha)+ Sin^{2}\frac{2\alpha}{3}*\frac{Cos^{2}\frac{2\alpha }{3}}{Sin^{2} \frac{2\alpha}{3}}+Sin^{2}\frac{2\alpha}{3} =\\\\=1-2+Cos^{2}\frac{2\alpha}{3}+Sin^{2}\frac{2\alpha}{3}=-1+1=0$

$2)tg(\frac{3\pi}{2}-\alpha)*tg(\pi+\alpha)+\frac{Sin^{4}\alpha+2Sin\alpha Cos\alpha-Cos^{4}\alpha}{Ctg(\frac{\pi}{2}-2\alpha)}=\\\\=Ctg\alpha*tg\alpha+\frac{(Sin^{2}\alpha-Cos^{2}\alpha)*(Sin^{2}\alpha+Cos^{2}\alpha)+2Sin\alpha Cos\alpha}{tg2\alpha}=\\\\=1-\frac{Cos2\alpha+Sin2\alpha}{tg2\alpha}$