Question

Prove the followings

Answer 1

Number 1 \[\frac{ \Delta }{ s-a }=s \tan \frac{ \alpha }{ 2 }\]

Answer 2

what does alpha , a , s , \(\Delta\) represent ?

Answer 3

\[\Delta=\sqrt{s(s-a)(s-b)(s-c)}\]

Answer 4

\[\tan \frac{ \alpha }{ 2 }=\sqrt{\frac{ (s-b)(s-c) }{ s(s-a) }}\]

Answer 5

right... got it now..

Answer 6

so now put these values :

\[\large{\frac{ \sqrt{s(s-a)(s-b)(s-c)}}{s-a} = \frac{\sqrt{s-a} \sqrt{s(s-b)(s-c)}}{s-a} }\]

Answer 7

prove it using either l.h.s or r.h.s

Answer 8

Yeah I am using LHS only

Answer 9

okay.. :)

Answer 10

well I can write :; \(\large{\frac{\sqrt{s-a}}{s-a} }\) as \(\frac{1}{\large{\sqrt{s-a}}}\)

Answer 11

therefore I get :

\[\large{\frac{\sqrt{s(s-b)(s-c)}}{\sqrt{s-a}}}\] = \[\large{\sqrt{\frac{(s-b)(s-c)s^2}{s(s-a)}}} \]

That is : \[\large{s\tan \frac{\alpha}{2}}\]

Answer 12

got it ?

Answer 13

can u prove it by multiplying and dividing trick i did'nt understand the roots u changed

Answer 14

like taking r.h.s and M & D it by \[\sqrt{s(s-a)}\]

Answer 15

see :