sin^4x+cos^4x=（sin^2x+cos^2x）²-2sin^2xcos^2x=1-2sin^2xcos^2x=1∴2sin^2xcos^2x = 0sinxcosx =0（sinx+cosx）²= sin^2x+cos^2x+2sinxcosx=1+2sinxcosx=1∴sinx+cosx=1