1.

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

Answer» `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)]`
`=4sinn(A/2)sin(B/2)cos(C/2)`
`N->sinA+sinB+sinC`
`=2sin((A+B)/2)cos((A-B)/2)+2sin(C/2)cos(C/2)`
`=2cos(C/2)cos((A-B)/2)+2sin(C/2)cos(C/2)`
`=2cos(C/2)[cos((A-B)/2)+cos((A+B)/2)]`
`=2cos(C/2)[2cos(A/2)cos(B/2)]`
`=4cos(A/2)cos(B/2)cos(C/2)`
`N/D=(4cos(A/2)cos(B/2)cos(C/2))/(4sin(A/2)sin(B/2)cos(C/2)`
`=cot(A/2)cot(B/2)`.


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