作业帮sin(45-3x)*cos(60-3x)-cos(30+3x)*sin(45+3x)
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/05/14 13:39:46
sin(45-3x)*cos(60-3x)-cos(30+3x)*sin(45+3x)
因为:sin(45-3x)=sin[90-(45+3x)]=cos(45+3x)
cos(60-3x)=cos[90-(30+3x)]=sin(30+3x).
则有
cos(45+3x)*sin(30+3x)-cos(30+3x)*sin(45+3x)
=sin(30+3x-45-3x)
=sin(-15)
=-sin15
=-sin(45-30)
=-[sin45*cos30-cos45*sin30]
=(√2-√6)/4.
cos(60-3x)=cos[90-(30+3x)]=sin(30+3x).
则有
cos(45+3x)*sin(30+3x)-cos(30+3x)*sin(45+3x)
=sin(30+3x-45-3x)
=sin(-15)
=-sin15
=-sin(45-30)
=-[sin45*cos30-cos45*sin30]
=(√2-√6)/4.
sin(45-3x)*cos(60-3x)-cos(30+3x)*sin(45+3x)
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