Question

Не знаю, как решить, весь день решаю....помогите

Answer 1

$1)frac{Sin^{2}alpha}{1-Sin^{2}alpha}*Ctg^{2}alpha=frac{Sin^{2}alpha}{Cos^{2}alpha}*Ctg^{2}alpha=tg^{2}alpha*Ctg^{2}alpha=1\\2)(Sinalpha-Cosalpha)^{2}+(Cosalpha+Sinalpha)^{2}=Sin^{2}alpha-2Sinalpha Cosalpha+Cos^{2}alpha+Cos^{2}alpha+2Sinalpha Cosalpha+Sin^{2}alpha=2Sin^{2}alpha+2Cos^{2}alpha=2(Sin^{2}alpha+Cos^{2}alpha)=2$

$3)frac{Sin^{2}alpha-tg^{2}alpha}{Cos^{2}alpha-Ctg^{2} alpha} =frac{Sin^{2}alpha-frac{Sin^{2}alpha}{Cos^{2}alpha}}{Cos^{2}alpha-frac{Cos^{2}alpha}{Sin^{2} alpha}}=frac{(Sin^{2}alpha Cos^{2}alpha-Sin^{2}alpha)*Sin^{2}alpha }{(Sin^{2}alpha Cos^{2}alpha-Cos^{2}alpha)*Cos^{2}alpha} =frac{Sin^{2}alpha(Cos^{2}alpha-1)*Sin^{2}alpha}{Cos^{2}alpha(Sin^{2}alpha-1)*Cos^{2}alpha}=frac{-Sin^{6}alpha}{-Cos^{6}alpha}=tg^{6}alpha$

$4)(1+tg^{2}alpha)(1-Sin^{2}alpha)=frac{1}{Cos^{2}alpha}*Cos^{2}alpha=1$

$5)frac{Sin^{3}alpha-Cos^{3}alpha}{Sinalpha-Cosalpha}-Sinalpha Cosalpha=frac{(Sinalpha-Cosalpha)(Sin^{2}alpha+Sinalpha Cosalpha+Cos^{2}alpha) }{Sinalpha-Cosalpha}-Sinalpha Cosalpha=1+Sinalpha Cosalpha-Sinalpha Cosalpha=1$