化简cos²(x/2-7π/8)-cos²(x/2+7π/8)

问题描述:

化简cos²(x/2-7π/8)-cos²(x/2+7π/8)

根据cos(2x)=2cos²(x)-1,所以原式=1/2【cos(x-7π/4)-1】-1/2【cos(x+7π/4)-1】
=1/2【cos(x-7π/4)-cos(x+7π/4)】=sin(7π/4)sinx=-sin(π/4)sinx=-2^(1/2) sinx.