(1)
sin^3a+cos^3a
=(sina+cosa)(sin^2a+cos^2a-sinacosa)
=(sina+cosa)(1-sinacosa)
因为sina+cosa=根号2,
所以(sina+cosa)^2=sin^2a+cos^2a+2sinacosa=1+2sinacosa=2
所以 sinacosa=1/2
所以原式=根号2*(1-1/2)=根号2/2
(2)tana+cota =sina/cosa + cosa/sina =(sin^2a+cos^2a)/sinacosa
=1/sinacosa
=2