已知函数f(x)=根号3cos(2x+φ)-sin(2x+φ)是奇函数,求φ值
问题描述：
已知函数f(x)=根号3cos(2x+φ)-sin(2x+φ)是奇函数,求φ值
答
f(x)=√3cos(2x+φ)-sin(2x+φ)
=2(√3/2cos(2x+φ)-1/2sin(2x+φ))
=2(cos(2x+φ)cosπ/6-sin(2x+φ)sinπ/6)
=2cos(2x+φ+π/6)
f(-x)=2cos(-2x+φ+π/6)=2cos(2x-(φ+π/6))
f(x)是奇函数,f(-x)=-f(x),即f(x)+f(-x)=0
2cos(2x+φ+π/6)+2cos(2x-φ-π/6)=0
2*2cos(2x)cos(φ+π/6)=0
cos(φ+π/6)=0
φ+π/6=2kπ+π/2
φ=2kπ+π/3