已知sinA+sinB=1/2,cosA+cosB=根号3/2,求证:sin(A+π/3)=1/2

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已知sinA+sinB=1/2,cosA+cosB=根号3/2,求证:sin(A+π/3)=1/2
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已知sinA+sinB=1/2,cosA+cosB=根号3/2,求证:sin(A+π/3)=1/2
已知sinA+sinB=1/2,cosA+cosB=根号3/2,求证:sin(A+π/3)=1/2

已知sinA+sinB=1/2,cosA+cosB=根号3/2,求证:sin(A+π/3)=1/2
对条件中两式求平方和得到:cos(A-B)=-1/2 (1) sin(A+π/3)=根号3/2*cosA+1/2*sinA =(cosA+cosB)cosA+(sinA+sinB)sinA =1+cos(A-B) =1/2 (将(1)代入)