Question

ПОМОГИТЕ СРОЧНО. 9 класс алгебра​

Answer 1

Решение задания приложено

Answer 2

$\frac{Cos378^{o}Sin27^{o}+Cos27^{o}Sin18^{o}}{Sin158^{o}Sin52^{o}+Cos52^{o}Cos22^{o}}=\frac{Cos(360^{0}+18^{o} )Sin27^{0}+Cos27^{2o}Sin18^{o}}{Sin(180^{o}-22^{o})Sin52^{o}+Cos52^{o}Cos22^{o}}=\frac{Cos18^{o}Sin27^{o} +Cos27^{o}Sin18^{o}}{Sin22^{o}Sin52^{o}+Cos52^{o}Cos22^{o}}=\frac{Sin(18^{o}+27^{o})}{Cos(52^{o}-22^{o})}=\frac{Sin45^{o} }{Cos30^{o}}=\frac{\sqrt{2}}{2}:\frac{\sqrt{3}}{2}=\frac{\sqrt{2}}{\sqrt{3}}=\frac{\sqrt{6}}{3}$

$\frac{Sin3\alpha+Sin7\alpha+Sin11\alpha}{Cos3\alpha+Cos7\alpha+Cos11\alpha}=\frac{(Sin3\alpha+Sin11\alpha)+Sin7\alpha}{(Cos3\alpha+Cos11\alpha)+Cos7\alpha}=\frac{2Sin7\alpha Cos4\alpha+Sin7\alpha}{2Cos7\alpha Cos4\alpha+Cos7\alpha}=\frac{Sin7\alpha(Cos4\alpha+1)}{Cos7\alpha(Cos4\alpha+1)}=\frac{Sin7\alpha}{Cos7\alpha}=tg7\alpha$

$\frac{tg74^{o}-tg14^{o}}{1+tg74^{o}tg14^{o}}=tg(74^{o}-14^{o})=tg60^{o}=\sqrt{3}$