化简1/2sin2x-1/2cos2x= (√2/2)sin(2x-π/4)

题目

化简1/2sin2x-1/2cos2x= (√2/2)sin(2x-π/4)
为什么要提取根2/2

答案

1/2sin2x-1/2cos2x=1/2(sin2xcosπ/4-cos2xsinπ/4)/(√2/2)=(√2/2)sin(2x-π/4)
不知楼主明白没?