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If A + B + C = pi and sin(A + C/2) = n s...

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)`

Text Solution

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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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