Sin(x/2)+cos(x/2)为什么等于根号2倍sin(x/2+派/4)?

Sin(x/2)+cos(x/2)为什么等于根号2倍sin(x/2+派/4)?
Sin(x/2)+cos(x/2)为什么等于根号2倍sin(x/2+派/4)?

Sin(x/2)+cos(x/2)为什么等于根号2倍sin(x/2+派/4)?
Sin(x/2)+cos(x/2)
=√2[√2/2sin(x/2)+√2/2cos(x/2)]
=√2[sin(x/2)cosπ/4+sinπ/4cos(x/2)]
=√2sin(x/2+π/4)

Sin(x/2)+cos(x/2)=√2[(√2/2)Sin(x/2)+(√2/2)cos(x/2)]
=√2[Sin(x/2)cos(π/4)+cos(x/2)sin(π/4)]
=√2Sin(x/2+π/4)