[tex]sin5 \alpha =5sin \alpha -20sin^3 \alpha +16sin^5 \alpha \\
Fie~ \alpha = \pi /5~si~x=sin \alpha .\\
sin \pi =0=5x-20x^3+16x^5\\
16x^4-20x^2+5=0\\
x^2=1/8(5\pm \sqrt{5} )\\
Dar~x=sin \pi /5~este~mai~mic~decat~sin \pi /4= \sqrt{2}/2\\
sin \pi /5= \sqrt{1/8(5- \sqrt{5} )}=1/4* \sqrt{10-2 \sqrt{5} } .[/tex]
