Question

In a ∆ABC if sides a,b and c are in A.P. Find Tan{A/2} Tan{C/2}​

Answer 1

$\huge{\underline{\sf{\red{Answer}}}}$

Given:

Sides of Triangle ABC a,b and c are in A.P

I.e 2b=a+c

$\huge{\underline{\tt{SoluTion}}}$

$\implies \sqrt{\dfrac{(s-b)\cancel{(s-c)}}{s(s-a)} \times \dfrac{\cancel{(s-a)}(s-b)}{s\cancel{(s-c)}}} \\ \\ \implies\sqrt\dfrac{ (s-b)(s-b)}{s\times s} \\ \\ \implies \dfrac{(s-b)}{s} \\ \\ \implies\dfrac{ 2s-2b}{2s} \\ \\ \implies \dfrac{a+b+c-2b}{a+b+c} \\ \\ \implies \dfrac{\cancel{a} + b +\cancel{c} -a-c }{a+b+c} \\ \\ \leadsto \dfrac{b}{3b} \\ \\ \huge\boxed{\dfrac{1}{3}}$