Question

Помогите пожалуйста решить !!!​

Answer 1

$1)frac{tgfrac{alpha}{4}Cosfrac{alpha}{4}}{1+Ctg^{2}frac{alpha}{4}}=frac{frac{Sinfrac{alpha}{4}}{Cosfrac{alpha}{4}}*Cosfrac{alpha}{4}}{frac{1}{Sin^{2}frac{alpha }{4}}} =Sinfrac{alpha}{4}*Sin^{2}frac{alpha}{4}=Sin^{3}frac{alpha}{4}$

$5)(tg3beta +Ctg3beta )*Sin^{2}3beta =(frac{Sin3beta}{Cos3beta}+frac{Cos3beta}{Sin3beta})*Sin^{2}3beta =frac{Sin^{2}3beta+Cos^{2}3beta}{Sin3beta Cos3beta}*Sin^{2}3beta =frac{1}{Sin3beta Cos3beta}*Sin^{2}3beta=frac{Sin3beta}{Cos3beta}=tg3beta$

$6)frac{Cos^{2}4alpha}{1+tg^{2}4alpha(Sin^{2}4alpha-1)}=frac{Cos^{2}4alpha}{1+tg^{2}4alpha*(-Cos^{2}4alpha)}= frac{Cos^{2}4alpha}{1-frac{Sin^{2}4alpha }{Cos^{2}4alpha}*Cos^{2}4alpha}=frac{Cos^{2}4alpha}{1-Sin^{2}4alpha}=frac{Cos^{2}4alpha}{Cos^{2}4alpha} =1$