sinα+cosβ=1/2,则sin^3α+cos^3β=

问题描述:

sinα+cosβ=1/2,则sin^3α+cos^3β=

sina+cosa=1/2(sina+cosa)²=1/4sin²a+2sinacosa+cos²a=1/41+2sinacosa=1/4sinacosa=-3/8sin³a+cos³a=(sina+cosa)×[sin²a-sinacosa+cos²a]=(1/2)×[1+(3/8)]=11/16...