If tan(A/2) = 5/6, tan(B/2) = 20/37, prove that a+c = 2b

Dear

we know

tanA/2 ={(s-b)(s-c)/s(s-a)}^1/2

tanB/2 ={(s-a)(s-c)/s(s-b)}^1/2

now first calculate

 tanA/2 * tanB/2 = 5/6  * 20/37

61a -161c + 61b =0   .................1

now calcualte

 tanA/2 / tanB/2  = 5/6 ÷ 20/37

put the value and simplify

 61a -13c -61b =0  ....................2

 now solve 1 and 2

a/87  = b/74 =c/61

 calculate a+c = [87/74 + 61/74 ]b

                     =2b

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