Question

онлайн мектеп алгебра

Answer 1

$1)\sqrt{2}(Cos27^{0}+Cos63^{0})=\sqrt{2}*2Cos\frac{27^{0}+63^{0}}{2}Cos\frac{27^{0}-63^{0}}{2} }=\\\\=2\sqrt{2}Cos45^{0} Cos18^{0}=2\sqrt{2} *\frac{1}{\sqrt{2} }*Cos18^{0}=\boxed{2Cos18^{0}}\\\\\\2)4\sqrt{2}(Sin27^{0}+Sin63^{0})=4\sqrt{2}*2Sin\frac{27^{0}+63^{0}}{2}Cos\frac{27^{0}-63^{0}}{2} }=\\\\=8\sqrt{2}Sin45^{0} Cos18^{0}=8\sqrt{2} *\frac{1}{\sqrt{2} }*Cos18^{0}=\boxed{8Cos18^{0}}$

$3)2\sqrt{2}(Cos27^{0}-Cos63^{0})=2\sqrt{2}*(-2Sin\frac{27^{0}+63^{0}}{2})Sin\frac{27^{0}-63^{0}}{2} }=\\\\=-4\sqrt{2}Sin45^{0}* (-Sin18^{0})=4\sqrt{2} *\frac{1}{\sqrt{2} }*Sin18^{0}=\boxed{4Sin18^{0}}$