1cos2(X/2-7π/8)-cos2(X/2+7π/8)

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1cos2(X/2-7π/8)-cos2(X/2+7π/8)1cos2(X/2-7π/8)-cos2(X/2+7π/8)1cos2(X/2-7π/8)-cos2(X/2+7π/8)原式={1+cos[

1cos2(X/2-7π/8)-cos2(X/2+7π/8)
1cos2(X/2-7π/8)-cos2(X/2+7π/8)

1cos2(X/2-7π/8)-cos2(X/2+7π/8)
原式={1+cos[2(x/2-7π/8)]}/2-{1+cos[2(x/2+7π/8)]}/2
=[1+cos(x-7π/4)]/2-[1+cos(x+7π/4)]/2
=1/2[cos(x-7π/4)-cos(x+7π/4)]
=1/2[(cosxcos7π/4+sinxsin7π/4)-(cosxcos7π/4-sinxsin7π/4)]
=sinxsin7π/4
=-√2(sinx)/2

原式=cos(x-7π/4)-cos(x+7π/4)
=cosxcos(7π/4)-sinxsin(7π/4)-(cosxcos7π/4-sinxsin7π/4)
==√2(cosx-sinx)