化简:{(1+sinx+cosx)[sin(x/2)-cos(x/2)}/根号下的(2+2cosx)

问题描述:

化简:{(1+sinx+cosx)[sin(x/2)-cos(x/2)}/根号下的(2+2cosx)

[1+2cosx/2*sinx/2+cos(x/2)^2-sin(x/2)^2 ][sin(x/2)-cos(x/2)]/根号下的[2*2cos(x/2)^2]
=2cos(x/2)[sin(x/2)+cos(x/2)][sin(x/2)-cos(x/2)]/2cos(x/2)
=-cosx