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In triangle A B C ,(sinA+sinB+sinC)/(sin...

In triangle `A B C ,(sinA+sinB+sinC)/(sinA+sinB-sinC)` is equal to

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`A+B+C=theta`
`sin((A+B)/2)=cos(C/2)`
`D->sinA+sinB-sinC`
`=2sin((A+B)/2)cos((A-B)/2)-sinC`
`=2cos(C/2)cos((A-B)/2)-2sin(C/2)cos(C/2)`
`=2cos(C/2)[cos((A-B)/2)-sin(C/2)]`
`=2cos(C/2)[cos((A-B)/2)-cos((A+B)/2)]`
`=2cos(C/2)[2sin(A/2)sin(B/2)]`
...
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