已知cos(15°+α)=15/17,α∈(0°,90°),求sin(15°-α)
问题描述：
已知cos(15°+α)=15/17,α∈(0°,90°),求sin(15°-α)
答
cos(15°+α)=15/17,sin(15°+α)=√1-cos^2(15°+α)=√1-(15/17)^2=8/17sin(15°-α)=sin[30°-(15°+α)]=sin30°cos(15°+α)-cos30°sin(15°+α)=1/2*15/17-√3/2*8/17=(15-8√3)/34