1.

In `DeltaABC`, prove that: `(a-b)/c=(sin(A-B)/(2))/(cosC/2)`

Answer» LHS `=(a-b)/c`
`=(ksinA-ksinB)/(ksinC)=(sinA-sinB)/(sinC)`
`=(2cos(A+B)/2.sin(A-B)/(2))/(2sinC/2.cosC/2)`
`=(cos(180^(2)-C)/(2)sin(A-B)/2)/(sinC/2cosC/2)` `(therefore A+B+C=180^(@))`
`=(cos(90^(2)-C/2)sin(A-B)/(2))/(sinC/2cosC/2)=(sinC/2.sin(A-B)/(2))/(sinC/2.cosC/2)`
`=(sin(A-B)/(2))/(cosC/2) = RHS` Hence Proved.


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