[by Neelanjan Mondal] At first use the inequality ,
, note that be equal to –,
must be equal to + and must be equal to . , that is for any acute angled triangle , put the values of , so we obtain ,
It is given that that is =
that is = .
So ,it is easy to say , .
So , we are done .
[Please note that , ]
Here , we have used a lemma (about the incircle , incenter…etc.) that is …
Note that = for any acute angled triangle , dividing by to the both sides , we get .
Now , = for the triangle .
Now we will express by the terms of .
so , = – ( = .That is equal to = .