已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+π/4)的值

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已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+π/4)的值
已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+π/4)的值

已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+π/4)的值
∵π/2≤a≤3π/2
∴cos(a+π/4)=3/5>0
∵a+π/4>3π/2
∴3π/2sin(a+π/4)=-√[1-cos²(a+π/4)]=-4/5
sina=[sin(a+π/4)-π/4]=√2/2*[sin(a+π/4)-cos(a+π/4)]=√2/2*(-4/5-3/5)=-7√2/10
cosa=-√(1-sin²a)=-√2/10
cos2a=2cos²a-1=-24/25,sin2a=2sinacosa=7/25
∴cos(2a+π/4)=√2/2(cos2a-sin2a)=-31√2/5