已知派/4<α<3派/4,0<β<派/4,cos(派/4-a)=3/5sin(3派/4+β)=5/13,求sin(a+β)
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已知π/4 0 3π/4<(3π/4+β)<π, 且sin(3π/4+β)=5/13所以cos(3π/4+β)=-12/13从而：sin(α+β)=cos[(3π/4+β)-(π/4-α)]=cos(3π/4+β)cos(π/4-α)+sin(3π/4+β)sin(π/4-α)=cos(3π/4+β)cos(π/4-α)-sin(3π/4+β)sin(α-π/4)=(-12/13)(3/5)-(5/13)(4/5)=-56/65