Sin^4a+cos^4a= если sina+cosa=1/корень из 2

Решите задачу:

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