sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5π/4),tan(b+5π/4)的值

问题描述:

sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5π/4),tan(b+5π/4)的值

根据sin(A-B)=sinAcosB-sinBcosA cos(b-a)=cosAcosB+sinAsinB ;
简化得到sinB=-3/5 可以得到cosB=-4/5 tanB=3/4
所以sin(B+5π/4)=sinBcos5π/4+cosBsin5π/4=-的根号2除以10;
tan(b+5π/4)=(tan5π/4+tanB)/(1-tan5π/4tanB) =5/8