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
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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/4)]-[B+(3π/4)]}=-sin[A-(π/4)]cos[B+(3π/4)]+cos[A-(π/4)]sin[B+(3π/4)]=56/65.即sin(A-B)=56/65.
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