Quadratic equation with the roots $\sin 18°, \cos 36°$ is

$\begin{array}{l}\alpha =\sin 18°=\frac{\sqrt{5}-1}{4},\beta =\cos 36°=\frac{\sqrt{5}+1}{4}\\ \text{Let\hspace{0.17em}}\alpha ,\beta \text{\hspace{0.17em}are the roots of quadratic equation}\\ \alpha +\beta =\frac{\sqrt{5}-1}{4}+\frac{\sqrt{5}+1}{4}=\frac{\sqrt{5}}{2}\\ \alpha \beta =\left(\frac{\sqrt{5}-1}{4}\right)\left(\frac{\sqrt{5}+1}{4}\right)=1\\ \text{Quadratic equation\hspace{0.17em}}{x}^2-\frac{\sqrt{5}}{2}x+1=0\\ 2x^2-\sqrt{5}x+2=0\end{array}$