cos^2 (x/2-7/8π)-cos^2(x/2+7π/8)可化简为?

问题描述:

cos^2 (x/2-7/8π)-cos^2(x/2+7π/8)可化简为?

原式=[1+(cosx-7/4π)]/2-[1+cos(x+7π/4)]/2
=(cosxcos7π/4+sinxsin7π/4)/2-(cosxcos7π/4-sinxsin7π/4)/2
=sinxsin7π/4
=(-√2/2)sinx