已知cos(丌/4-a)=3/5sin(5/4丌+b)=-12/13a属于(丌/4,3丌/4)b属于(0,丌/4)求sin(a+b)的值
问题描述:
已知cos(丌/4-a)=3/5sin(5/4丌+b)=-12/13a属于(丌/4,3丌/4)b属于(0,丌/4)求sin(a+b)的值
答
∵ sin(3π/4 +b)=cos[π/2-(3π/4 +b)]=cos(-π/4-b)=cos(π/4+b)=5/13a∈(π/4,3π/4),b∈(0,π/4)∴π/4 -a∈(-π/2,0),π/4+b∈(π/4,π/2)∴sin(π/4 -a)<0,sin(π/4+b)>0∴sin(π/4 -a)...