已知f(x)=2sin(x+θ/2)cos(x+θ/2)+2√3cos²(x+θ/2)-√3,且0≤θ≤π,求使函数f(x)为偶函数的值
问题描述:
已知f(x)=2sin(x+θ/2)cos(x+θ/2)+2√3cos²(x+θ/2)-√3,且0≤θ≤π,求使函数f(x)为偶函数的值
答
f(x)=sin(2x+θ)+2√3[1+cos(2x+θ)]/2-√3=sin(2x+θ)+√3cos(2x+θ)=2sin(2x+θ+π/3)是偶函数f(-x)=f(x)2sin(-2x+θ+π/3)=2sin(2x+θ+π/3)所以-2x+θ+π/3=2kπ+2x+θ+π/3或-2x+θ+π/3=2kπ+π-(2x+θ+π/3)-...