Найдите sin3a + cos3a, если sin a - cos a= 1/ корень из 2

[latex]sina-cosa=\frac{\sqrt{2}}{2}\\ [/latex] [latex]sin3a+cos3a=\\4cos^3a-3cosa+3sina-4sin^3a=\\ 4(cos^3a-sin^3a)+3(sina-cosa)=\\ -4(sina-cosa)(cos^2a+cosa*sina+sin^2a)+3(sina-cosa)=\\ \\ (sina-cosa)^2=1-2cosa*sina=\frac{1}{2}\\ cosa*sina=\frac{1}{4}\\ \\ sin3a+cos3a=-4*\frac{\sqrt{2}}{2}(1+\frac{1}{4})+3\frac{\sqrt{2}}{2}=-\sqrt{2}*\frac{5}{2}+3*\frac{\sqrt{2}}{2}=\frac{3\sqrt{2}-5\sqrt{2}}{2}=-\sqrt{2}[/latex]