Question

√3sin(100πt+π/3)+sin(100πt-π/6)化简

Answer 1

因为　100πt+π/3= π/2+ (100πt-π/6)
所以　sin(100πt+π/3)=sin[π/2 +(100πt -π/6)]=cos(100πt- π/6)
所以　
原式=√3cos(100πt-π/6)+sin(100πt-π/6)
=2[(√3/2)·cos(100πt-π/6)+(1/2)·sin(100πt-π/6)]
=2sin(100πt-π/6+π/3)
=2sin(100πt+π/6)

追问

为什么100πt+π/3= π/2+ (100πt-π/6)

追答

因为　π/3= π/2- π/6

追问

为什么2[(√3/2)·cos(100πt-π/6)+(1/2)·sin(100πt-π/6)]
=2sin(100πt-π/6+π/3)

追答

(√3/2)·cos(100πt-π/6)+(1/2)·sin(100πt-π/6)
=sin(π/3)·cos(100πt-π/6)+cos(π/3)·sin(100πt-π/6)
=sin(100πt-π/6+π/3)，
这是两角和的正弦公式．