(1-cos2x)+sin2x=根号2(sin2x cosπ/4-cos2x sinπ/4)+1 这个是怎么化简得的?_数学解答

(1-cos2x)+sin2x=根号2(sin2x cosπ/4-cos2x sinπ/4)+1 这个是怎么化简得的?

人气：489 ℃　时间：2019-12-07 03:18:25

解答

sin2x-cos2x
=√2(sin2x*√2/2-cos2x*√2/2)
=√2(sin2xcosπ/4-cos2xsinπ/4)
=√2sin(2x-π/4)
这里用到 sinπ/4=cosπ/4=√2/2