化简sin(π+π⼀3)+2sin(x-π⼀3)-根号下3 *cos(2π⼀3-x)

2025-04-03 11:20:33
推荐回答(1个)
回答1:

sin(x+π/3)=sinxcos(π/3)+cosxsin(π/3)=1/2sinx+√3/2cosx
2sin(x-π/3)=2sinxcos(π/3)-2cosxsin(π/3)=sinx+√3cosx
-√3cos(2π/3-x)=-√3(cos(2π/3)cosx+sin(2π/3)sinx)=-√3(-1/2cosx+√3/2sinx)=√3/2cosx-3/2xsinx
把上面三个式子加起来就是2√3cosx