Question

sin^4a+cos^4a=

если sina+cosa=1/корень из 2

Answer 1

$sina+cosa= frac{1}{sqrt2}\\\(sina+cosa)^2= frac{1}{2} \\underline {sin^2a}+2sina, cosa+underline {cos^2a}=frac{1}{2}\\1+2sinacdot cosa=frac{1}{2} ; ; to ; ; ; 2sinacdot cosa=-frac{1}{2}; ,; ; sinacdot cosa=-frac{1}{4}\\\1=sin^2a+cos^2a\\1^2=(sin^2a+cos^2a)^2\\1=sin^4a+2sin^2acdot cos^2a+cos^4a; ; to \\sin^4a+cos^4a=1-2(sinacdot cosa)^2=1-2cdot (-frac{1}{4})^2=1-2cdot frac{1}{16}; ,\\\sin^4a+cos^4a=1-frac{1}{8}=frac{7}{8}$