已知f(x)=2sin(2x+π/6).若f(x1)=6\5,x1属于【π/4,π/2】,则cos2x1=?
问题描述：
已知f(x)=2sin(2x+π/6).若f(x1)=6\5,x1属于【π/4,π/2】,则cos2x1=?
答
sin(2x1+π/6)=3/5,x1属于【π/4,π/2】,cos(2x1+π/6)=-4/5cos2x1=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