Question

СРОЧНО!!!!!

Помогите упростить

Answer 1

$5)frac{tg^{2}alpha}{1+tg^{2} alpha }*frac{1+Ctg^{2}alpha}{Ctg^{2}alpha} =frac{tg^{2}alpha}{frac{1}{Cos^{2}alpha} }*frac{frac{1}{Sin^{2}alpha} }{Ctg^{2}alpha}=frac{Sin^{2}alpha *Cos^{2}alpha}{Cos^{2}alpha }*frac{Sin^{2}alpha}{Sin^{2} alpha*Cos^{2} alpha}=Sin^{2}alpha*frac{1}{Cos^{2} alpha }=frac{Sin^{2}alpha}{Cos^{2}alpha}=tg^{2}alpha$

$6)frac{1+tgalpha }{1+Ctgalpha }=frac{1+frac{Sinalpha }{Cosalpha } }{1+frac{Cosalpha }{Sinalpha } }=frac{frac{Cosalpha+Sinalpha }{Cosalpha } }{frac{Cosalpha+Sinalpha  }{Sinalpha } }=frac{(Cosalpha+Sinalpha )*Sinalpha  }{(Cosalpha+Sinalpha)*Cosalpha} =frac{Sinalpha }{Cosalpha } =tgalpha$

$7)Cos^{4}alpha+Sin^{2}alpha Cos^{2} alpha-Cos^{2}alpha -1=(Cos^{4}alpha+Sin^{2}alpha Cos^{2}alpha)-Cos^{2}alpha-1=Cos^{2}alpha(Cos^{2} alpha+Sin^{2}alpha)-Cos^{2}alpha-1=Cos^{2}alpha*1-Cos^{2} alpha -1=Cos^{2}alpha-Cos^{2}alpha -1=-1$