y=sin(π/3-2x)+cos(2x)的周期怎么求?

题目

y=sin(π/3-2x)+cos(2x)的周期怎么求?

答案

y=sin(π/3-2x)+cos(2x)=—sin(2x)cosπ/3+cos2xsinπ/3+cos(2x)
由于cosπ/3=1/2,sinπ/3=√3/2.则有y=—1/2sin(2x)+(√3+2)/2cos(2x)
令tanb==—1/(√3+2),则有y=sin(2x+b).则有T=π