Question

Sin^6a+cos^6a если sina-cosa=0,3

Answer 1

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