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函数y=4sin(wx+π/4)cos(wx-π/4)-2sin(wx-π/4)cos(wx+π/4)(w>0)化简
题目详情
函数y=4sin(wx +π/4)cos(wx-π/4)-2sin(wx-π/4)cos(wx+π/4)(w>0)化简
▼优质解答
答案和解析
y=2sin(wx+π/4)cos(wx-π/4)-2cos(wx+π/4)sin(wx-π/4)+2sin(wx+π/4)cos(wx-π/4)
=2sin[(wx+π/4)-(wx-π/4)]+2sin(wx+π/2-π/4)cos(wx-π/4)
=2sin(π/2)+2cos²(wx-π/4)
=2+2cos²(wx-π/4)
=3+2cos²(wx-π/4)-1
=cos(2wx-π/2)+3
=sin2wx+3
=2sin[(wx+π/4)-(wx-π/4)]+2sin(wx+π/2-π/4)cos(wx-π/4)
=2sin(π/2)+2cos²(wx-π/4)
=2+2cos²(wx-π/4)
=3+2cos²(wx-π/4)-1
=cos(2wx-π/2)+3
=sin2wx+3
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