Question

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

Answer 1

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