Question

помогете решать пожалуйста 8sin9*sin81*sin54

Answer 1

$8Sin9^{0}*Sin81^{0}*Sin54^{0}=8Sin9^{0}*Sin(90^{0} -9^{0} )*Sin54^{0}=4(2Sin9^{0} Cos9^{0} )*Sin54^{0} =4Sin18^{0}Sin54^{0} =4Sin18^{0}*Sin(90^{0} -36^{0})=4Sin18^{0}Cos36^{0}=4*\frac{2Cos18^{0}Sin18^{0}Cos36^{0}}{2Cos18^{0}}=\frac{4Sin36^{0}Cos36^{0}}{2Cos18^{0}}=\frac{Sin72^{0}}{Cos18^{0}}=\frac{Sin(90^{0}-18^{0})}{Cos18^{0}}=\frac{Cos18^{0} }{Cos18^{0}}=1$