Question

кто сможет? обьясните пожалуйста​

Answer 1

$4Sin^{2}18^\circ =\dfrac{2Sin18^\circ\cdot 2Sin18^\circ\cdot Cos18^\circ }{Cos18^\circ} =\dfrac{2Sin18^\circ\cdot Sin36^\circ}{Cos18^\circ} =\\\\=\dfrac{2\cdot \frac{1}{2}[Cos(18^\circ - 36^\circ)-Cos(18^\circ+36^\circ)] }{Cos18^\circ} =\dfrac{Cos18^\circ-Cos54^\circ}{Cos18^\circ } =\\\\=1-\dfrac{Cos54^\circ}{Cos18^\circ}=1-\dfrac{Cos(90^\circ-36^\circ)}{Cos18^\circ}=1-\dfrac{Sin36^\circ}{Cos18^\circ}=\\\\=1-\dfrac{2Sin18^\circ Cos18^\circ}{Cos18^\circ}=1-2Sin18^\circ$

$\underbrace{4Sin^{2}18^\circ}_{1-2Sin18^\circ} +2Sin18^\circ+2,5=1-2Sin18^\circ+2Sin18^\circ+2,5=\\\\=1+2,5=\boxed{3,5}$