sin(2x－π/4)－2√2sin^2x 怎么化简?

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/26 06:56:39

sin(2x－π/4)－2√2sin^2x 怎么化简?
后面2√2sin^2 x 2是平方，x是在下面的。。。2倍根号2乘以sin的平方乘x
我化到原式＝√2/2sin2x－√2/2cos2x-√2+√2cos2x

sin(2x－π/4)－2√2sin^2x
=sin2xcos(π/4)-cos2xsin(π/4)-√2(1-cos2x)
=√2/2(sin2x+cos2x)-√2
=sin(2x+π/4)-√2
再问： =√2/2(sin2x+cos2x)-√2 =sin(2x+π/4)-√2 就是这两步不懂，
再答： sinπ/4=cosπ/4=√2/2, sin(A+B)=sinAcosB+cosAsinB √2/2(sin2x+cos2x)-√2 =sin2xcosπ/4+cos2xsinπ/4-√2 =sin(2x+π/4)-√2 看明白吗？你要记住一些基本公式哦。祝你进步！
再问：晕，，，，居然没想到同时提取2√2………谢了哈～

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