Question

Prove:
Δ/s-a = s*tan a/2

Answer 1

\[\frac{ Δ }{ s-a } = s \tan \frac{ \alpha }{ 2 }\]

Answer 2

using R.H.S ??

Answer 3

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

Answer 4

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

Answer 5

then its direct.
\(\dfrac{\Delta}{s-a} =\dfrac{ \sqrt{s(s-a)(s-b)(s-c)}}{s-a}=\dfrac{ \sqrt{s(s-b)(s-c)}}{\sqrt{s-a}}\)

Answer 6

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

Answer 7

LHS = RHS.

Answer 8

we have to prove it using a single side

Answer 9

okk.

Answer 10

i think we should choose R.H.S

Answer 11

any1 can be chosen.,
\(\dfrac{\Delta}{s-a} =\dfrac{ \sqrt{s(s-a)(s-b)(s-c)}}{s-a}\\ =\dfrac{ \sqrt{s(s-b)(s-c)}}{\sqrt{s-a}} \\=\sqrt{\frac{s (s-b)(s-c) }{ (s-a) }} \\ =s \sqrt{\frac{ (s-b)(s-c) }{ s(s-a) }} \\ = s\tan \frac{ \alpha }{ 2 } \)

Answer 12

WHAT HAPPENED IN THE SECOND STEP WITH s-a ???

Answer 13

\(\dfrac{\sqrt{s-a}}{s-a}=\dfrac{1}{\sqrt{s-a}}\)