Question

(ctg(6,5pi - a) * cos(-a) * tg(5pi/2 +a))² - ctg(pi-a)/tg²(a-pi)

Answer 1

$\Big (ctg(6,5\pi -a)\cdot cos(-a)\cdot tg(\frac{5\pi}{2}+a)\Big )^2-\frac{ctg(\pi -a)}{tg^2(a-\pi )}=\\\\=\Big (ctg(6\pi +\frac{\pi}{2}-a)\cdot cosa\cdot (-ctga)\Big )^2-\frac{-ctga}{tg^2(\pi -a)}=\\\\=\Big (-tga\cdot cosa\cdot ctga\Big )^2+\frac{ctga}{tg^2a}=(-cosa)^2+\frac{1}{tg^3a}=\\\\=cos^2a+\frac{1}{tg^3a}$