sin^3X+cos^3X
=（sinx+cosx)(sin^2x-sinxcosx+cos^2x)
=根号2(1+sinxcosx)
sinX+cosX=根号2
所以sin^2x+cos^2x+2sinxcosx=2所以sinxcosx=1/2
所以原式等于（根号2）/2