已知cos（75゜+α）=3/5，180゜<α<270゜，求sin(30゜-2α)-cos(α-45゜)的值

∵180゜<α<270゜
∴255゜<75゜+α<345゜
∴∠(75+α゜)的终边∈Ⅲ、Ⅳ
又∵cos（75゜+α）=3/5>0
∴ ∠(75゜+α)的终边在第四象限
∴270゜<75゜+α<360゜
∴-360゜<-75゜-α<-270゜
∴-360゜+90゜<-75゜-α+90゜<-270゜+90゜，-270゜<15゜-α<-180゜
∴∠(15゜-α)的终边∈Ⅱ
又∵sin(15゜-α)=cos[90゜-(15゜-α)]=cos(75゜+α)=3/5
∴cos(15゜-α)=-√[1-(sin^2)(15゜-α)]=-√[1-(3/5)^2]=-4/5
∴sin(30゜-2α)=2sin(15゜-α)cos(15゜-α)=2*(3/5)*(-4/5)=-24/25
cos(α-45゜)=cos(45゜-α)=cos[(15゜-α)+30゜]
=cos(15゜-α)cos30゜-sin(15゜-α)sin30゜
=(-4/5) ×(√3)/2-(3/5) ×(1/2)
=-(2√3)/5-3/10
∴ sin(30゜-2α)-cos(α-45゜)
=-24/25+2(√3)/5+3/10
=(2√3)/5-33/50
=[(20√3)-33]/50