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cos(x＋π/4)cos(x-π/4)怎么化简
题目详情
cos(x＋π/4)cos(x-π/4)怎么化简
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答案和解析
因为cos(x+π/4)=cos(x+π/2-π/4)=cos[π/2+(x-π/4)]=-sin(x-π/4)
所以 cos(x＋π/4)cos(x-π/4)
=-sin(x-π/4)cos(x-π/4)
=-1/2sin(2x-π/2)
=1/2cos2x
所以 cos(x＋π/4)cos(x-π/4)
=-sin(x-π/4)cos(x-π/4)
=-1/2sin(2x-π/2)
=1/2cos2x
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