Sin^6a+cos^6a если sina-cosa=0,3

[latex]sina-cosa=0,3\\\\1)\; \; (sina-cosa)^2=sin^2a-2sina\cdot cosa+cos^2a=1-2sina\cdot cosa\\\\0,3^2=1-2sina\cdot cosa\; \; \to \; \; sina\cdot cosa=\frac{1}{2}(1-0,09)=0,455\\\\2)\; \; 1=(sin^2a+cos^2a)^3=\\\\=sin^6a+cos^6a+3sin^4a\cdot cos^2a+3sin^2a\cdot cos^4a=\\\\=sin^6a+cos^6a+3sin^2a\cdot cos^2a(sin^2a+cos^2a)=\\\\=sin^6a+cos^6a+3\cdot 0,455^2\cdot 1=sin^6a+cos^6a+0,621075\; \to \\\\sin^6a+cos^6a=1-0,621075\\\\sin^6a+cos^6a=0,378925[/latex]