If `A + B + C = pi` and `sin(A + C/2) = n sin(C/2)`, show that `tan(A/ – InterviewSolution

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1.	If `A + B + C = pi` and `sin(A + C/2) = n sin(C/2)`, show that `tan(A/2). tan(B/2) = (n-1)/(n+1)`
Answer» RHS `(n-1)/(n+1)` `((sin(A+C/2)-sinC/2)/(sin(C/2)))/((sinn(A+C/2)+sin(C/2))/sin(C/2))` `(2cos((A+C)/2)sin(A/2))/(2sin((A+C)/2)cos(A/2)` `cot((A+C)/2)tan(A/2)` `cot((pi-B)/2)tan(A/2)` `tan(B/2)*tan(A/2)` LHS.

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