prove that if in triangle ABC tan(A/2)=5/6 tan(B/2)=2/5 then a,b,c will be in AP

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- December 28th 2010, 09:39 AMprasumtrigo help
prove that if in triangle ABC tan(A/2)=5/6 tan(B/2)=2/5 then a,b,c will be in AP

- December 28th 2010, 10:04 AMBAdhi
what's "AP"

- December 28th 2010, 10:04 AMPlato
- December 29th 2010, 04:44 AMprasum
i have found tan A and Tan B through tan2A formula after that i have found out Tan C by Tan A+TanB+TanC=TanATanBTanC brcause A+b+c=180 degrees after that how should i find a,b,c and prove they are in arithmetic progression

- December 29th 2010, 09:13 AMBAdhi
wouldn't and work?

- December 30th 2010, 07:18 AMArchie Meade

We obtain the cosines from Pythagoras' Theorem.

From the Law of Sines

If a, b, and c are in Arithmetic progression,

then the sum of the 3 sides is 3 times the "middle side".

Hence, the sum of the 3 sines must be 3 times the sum of the "middle sine".

Therefore

a, c, b are in Arithmetic Progression.

b, c, a are in Arithmetic Progression.