Question

упростите:sin18*cos36=

Answer 1

$Sin18^{o} *Cos36^{0} =\frac{2Cos18^{0}*Sin18^{0}*Cos36^{o}}{2Cos18^{0}}=\frac{Sin36^{0}*Cos36^{0}}{2Cos18^{o}}=\frac{2*Sin36^{0}*Cos36^{0}}{2*2Cos18^{0} }=\\\\=\frac{Sin72^{0}}{4Cos18^{0}}=\frac{Sin(90^{0}-18^{0})}{4Cos18^{0}}=\frac{Cos18^{o}}{4Cos18^{0}}=\frac{1}{4}=0,25\\\\Otvet:\boxed{0,25}$