Question

Пожалуйста помогите, нужно доказать тождество плиз срочно! Люди добрые помогите!

Answer 1

$2)\frac{Sin34^{o}*Cos16^{o}-Sin56^{o}Sin16^{o}}{Sin8^{o}*Sin80^{o} +Cos82^{o}*Cos10^{o}}=\frac{Sin34^{o}Cos16^{0}-Cos34^{o}Sin16^{o}}{Sin8^{o}Cos10^{o}+Sin8^{o}Cos10^{o}}=\frac{Sin(34^{0}-16^{o})}{Sin(8^{0}+10^{o})} =\frac{Sin18^{o} }{Sin18^{o}}=1\\\\1=1$

$3)tg^{4}\alpha[8Sin^{2}(\alpha+\frac{3\pi }{2})-Sin(4\alpha-\frac{\pi }{2})-1]=tg^{4}\alpha[8Cos^{2}\alpha+Sin(\frac{\pi }{2}-4\alpha)-1] =tg^{4}\alpha[8Cos^{2}\alpha+Cos4\alpha-1]=tg^{4}\alpha (8Cos^{2}\alpha-2Sin^{2}2\alpha)=tg^{4}\alpha(8Cos^{2}\alpha-8Sin^{2}\alpha Cos^{2}\alpha                              )=tg^{4}\alpha[(8Cos^{2}\alpha (1 -Sin^{2}\alpha)]=tg^{4}\alpha *8Cos^{4}\alpha=\frac{Sin^{4}\alpha}{Cos^{4}\alpha}*8Cos^{4}\alpha=8Sin^{4}\alpha\\\\8Sin^{4}\alpha=8Sin^{4}\alpha$