Question

26.10 пожалуйста весь срочно

Answer 1

$1)4Sin^{2} 1^{o}Cos^{2} 1^{o} -Cos^{2}2^{o}=Sin^{2}2^{o}-Cos^{2}2^{o}=-Cos4^{o}\\\\2)16Sin^{2}3^{o}Cos^{2}3^{o}Cos^{2}6^{o} =4Sin^{2}6^{o}Cos^{2}6^{o}=Sin^{2}12^{o}$

$3)(Sin10^{o}+Sin80^{o})(Cos80^{o}-Cos10^{o})=(Sin10^{o}+Sin(90^{o}-10^{o}))(Cos(90^{o}-10^{o})-Cos10^{o})=(Sin10^{o}+Cos10^{o})(Sin10^{o}-Cos10^{o})=Sin^{2}10^{o} -Cos^{2}10^{o} =-Cos20^{0}$

$4)(Cos5^{o} +Cos95^{o})(Sin85^{o}+Sin175^{o} )=(Cos5^{o}+Cos(90^{o}+5^{o}))(Sin(90^{o}-5^{o})+Sin(180^{o}-5^{o} )) } =(Cos5^{o}-Sin5^{o})(Cos5^{o}+Sin5^{o})=Cos^{2}5^{o}-Sin^{2}5^{o}=Cos10^{o}$

$5)\frac{Cos^{2}36^{o}+Sin^{2}18^{o}}{Cos^{2}18^{o}}=\frac{1-2Sin^{2}18^{o} +Sin^{2}18^{o}}{Cos^{2}18^{o}}=\frac{1-Sin^{2}18^{o}}{Cos^{2}18^{o}}=\frac{Cos^{2}18^{o}}{Cos^{2}18^{o}}=1$

$6)\frac{Cos56^{o} }{Cos28^{o}+Sin28^{o}}+Sin28^{o} =\frac{Cos^{2}28^{o}-Sin^{2}28^{o}}{Cos28^{o}+Sin28^{o}}+Sin28^{o} =\frac{(Cos28^{o}+Sin28^{o})(Cos28^{o}-Sin28^{o})}{Cos28^{o}+Sin28^{o}}+Sin28^{o}=Cos28^{o}-Sin28^{o}+Sin28^{o}=Cos28^{o}$