sina+cosa=√2sin（a+π/4）=1a=2kπ或π/2+2kπ∴sin^6a+cos^6a=0+1=1
sina+cosa=1(sina+cosa)^2=1sina^2+cosa^2+2sinacosa=1又sina^2+cosa^2=1所以2sinacosa=0所以sina=1 cosa=0 或者sina=0 cosa=1所以sin^6a+cos^6a=1
