sin(45-3x)*cos(60-3x)-cos(30+3x)*sin(45+3x)

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sin(45-3x)*cos(60-3x)-cos(30+3x)*sin(45+3x)sin(45-3x)*cos(60-3x)-cos(30+3x)*sin(45+3x)sin(45-3x)*cos

sin(45-3x)*cos(60-3x)-cos(30+3x)*sin(45+3x)
sin(45-3x)*cos(60-3x)-cos(30+3x)*sin(45+3x)

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.

sin(45-3x)*cos(60-3x)-cos(30+3x)*sin(45+3x)
=cos[90-(45-3x)]sin[90-(60-3x)]-cos(30+3x)sin(45+3x)
=sin(30+3x)*cos(45+3x)-cos(30+3x)*sin(45+3x)
=sin(30-45)
=sin30cos45-sin45cos30
=(1/2)(√2/2)-(√2/2)(√3/2)
=(√2-√6)/4