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_数学解答

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

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解答

∵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...