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)
答
原式=[cos(x/2-7π/8)+cos(x/2+7π/8)]cos(x/2-7π/8)-cos(x/2+7π/8)].
=2cos(x/2)cos(-7π/4)*[-2sin(x/2)sin(-7π/4)].
=2sin(x/2)cos(x/2)*[2sin(+7π/4)cos(-7π/4).
=sinx*2sin(7/4)cos(7π/4).
=sinxsin(7π/2).
=sinx*sin(4-π/2).
=sinx*sin(-π/2).
=-sinx.
答
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.