为什么f(x)=sin(2x- π/3 )+√3 cos(2x- π/3 )=2sin2x能不能列出详细的过程,感激不尽
问题描述：
为什么f(x)=sin(2x- π/3 )+√3 cos(2x- π/3 )=2sin2x
能不能列出详细的过程,感激不尽
答
f(x)=sin(2x- π/3 )+√3 cos(2x- π/3 )=2[1/2sin(2x- π/3 )+√3 /2cos(2x- π/3 )]=2[cosπ/3 sin(2x- π/3 )+sinπ/3 cos(2x- π/3 )]=2sin2x
答
将（2x-π/3）看成一个变量设为m
则f(x)=sinm+√3cosm=(√[(√3)^2+1^2])(1/2sinm+(√3)/2cosm)=2(sinmcos(π/3)+cosmsin(π/3))
=2sin(m+π/3)将m带入有
=2sin[(2x-π/3)+π/3]=2sin2x