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已知f(x)=2sin(2x+π/6).若f(x1)=6\5,x1属于π/4,π/2,则cos2x1=?
题目详情
已知f(x)=2sin(2x+π/6).若f(x1)=6\5,x1属于【π/4,π/2】,则cos2x1=?
▼优质解答
答案和解析
sin(2x1+π/6)=3/5,x1属于【π/4,π/2】,cos(2x1+π/6)=-4/5
cos2x1=sin(π/2-2x1)
=-sin(2x1+π/6-2π/3)
=-sin(2x1+π/6)cos(-2Pi/3)+cos(2x1+π/6)sin(-2Pi/3)
=-3/5(-1/2)+(-4/5)(-3^0.5/2)
=3/10+2/5*3^0.5
cos2x1=sin(π/2-2x1)
=-sin(2x1+π/6-2π/3)
=-sin(2x1+π/6)cos(-2Pi/3)+cos(2x1+π/6)sin(-2Pi/3)
=-3/5(-1/2)+(-4/5)(-3^0.5/2)
=3/10+2/5*3^0.5
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