sin(a-b)=5/13,sin(a+b)= -5/13且a-b∈(π/2,π),a+b∈(3π/2,2π),求cos2b的值

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sin(a-b)=5/13,sin(a+b)=-5/13且a-b∈(π/2,π),a+b∈(3π/2,2π),求cos2b的值sin(a-b)=5/13,sin(a+b)=-5/13且a-b∈(π/2

sin(a-b)=5/13,sin(a+b)= -5/13且a-b∈(π/2,π),a+b∈(3π/2,2π),求cos2b的值
sin(a-b)=5/13,sin(a+b)= -5/13且a-b∈(π/2,π),a+b∈(3π/2,2π),求cos2b的值

sin(a-b)=5/13,sin(a+b)= -5/13且a-b∈(π/2,π),a+b∈(3π/2,2π),求cos2b的值
cos2b=cos[(a+b)-(a-b)]=cos(a+b)cos(a-b)+sin(a+b)sin(a-b)
cos(a-b)=-12/13,cos(a+b)=12/13代入求值即可.