f(x)=sin (ωx+φ)+cos(ωx+φ) =√2sin (ωx+φ+π/4)

问题描述:

f(x)=sin (ωx+φ)+cos(ωx+φ) =√2sin (ωx+φ+π/4)
这步是如何化简过来的!

f(x)=sin (ωx+φ)+cos(ωx+φ)
【每项乘以一个√2,再除以一个√2(sinπ/4=cosπ/4=1/√2)】得到
=√2cosπ/4sin (ωx+φ)+√2sinπ/4cos(ωx+φ)
=√2[ cosπ/4sin (ωx+φ)+sinπ/4cos(ωx+φ)]
利用公式sinacosb+cosasinb=sin(a+b),本题a=ωx+φ,b=π/4
=√2sin (ωx+φ+π/4)