已知函数f(x)=2√3sinx-2cosx(2)若f(x)=0,求2cos^2-sinx-1/√2sin(x+π/4)的值

f(x)=2√3sinx-2cosx若f(x)=0,即 2√3sinx-2cosx=0∴√3sinx-cosx=0∴tanx=√3/3∴x=2kπ+π/6,或x=2kπ+7π/6,k∈Z当x=2kπ+π/6,k∈Z,时cosx=√3/2,sinx=1/2(2cos²x-sinx-1)/√2sin(x+π/4)=(2cos²x-sin...