已知0<B<π/4<A<3/4π,且COS(π/4-A)=4/5,SIN(3π/4+B)=5/13,求sin(A—B)的值

问题描述:

已知0<B<π/4<A<3/4π,且COS(π/4-A)=4/5,SIN(3π/4+B)=5/13,求sin(A—B)的值

∵0<B<π/4<A<3π/4.∴0<A-(π/4)<π/2.3π/4<B+(3π/4)<π.又cos[A-(π/4)]=4/5,sin[B+(3π/4)]=5/13.∴sin[A-(π/4)]=3/5,cos[B+(3π/4)]=-12/13.∴sin(A-B)=sin{[(A-(π/4)]-[B+(3π/4)]+π}=-sin{[A-(π...