化简cos²(x/2-7π/8)-cos²(x/2+7π/8)

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化简cos²(x/2-7π/8)-cos²(x/2+7π/8)化简cos²(x/2-7π/8)-cos²(x/2+7π/8)化简cos²(x/2-7π

化简cos²(x/2-7π/8)-cos²(x/2+7π/8)
化简cos²(x/2-7π/8)-cos²(x/2+7π/8)

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.

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...

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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.

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