[latex]sin alpha cos alpha =frac{sqrt{3}}{4}\ \ sin alpha =frac{sqrt{3}}{4}cos alpha \ sin^2 alpha +cos alpha =1\ (frac{sqrt{3}}{4}cos alpha )^2+cos^2 alpha =1\ frac{3}{16}cos^2 alpha +cos^2 alpha =1\ frac{19}{16}cos^2 alpha =1\ cos^2 alpha =frac{16}{19}\ cos alpha =sqrt{frac{16}{19}}=frac{4}{sqrt{19}}\ \ sin alpha =frac{sqrt{3}}{4}cdot frac{4}{sqrt{19}}=frac{sqrt{3}}{sqrt{19}}\ \ [/latex] [latex]sin ^4 alpha + cos ^4 alpha = (frac{sqrt{3}}{sqrt{19}})^4+(frac{4}{sqrt{19}})^4 = (frac{3}{19})^2+(frac{16}{19})^2=\=frac{9}{361}+frac{256}{361}=frac{265}{361}[/latex]
