anonymous
  • anonymous
Prove the followings
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Number 1 \[\frac{ \Delta }{ s-a }=s \tan \frac{ \alpha }{ 2 }\]
mathslover
  • mathslover
what does alpha , a , s , \(\Delta\) represent ?
anonymous
  • anonymous
\[\Delta=\sqrt{s(s-a)(s-b)(s-c)}\]

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anonymous
  • anonymous
\[\tan \frac{ \alpha }{ 2 }=\sqrt{\frac{ (s-b)(s-c) }{ s(s-a) }}\]
mathslover
  • mathslover
right... got it now..
mathslover
  • mathslover
so now put these values : \[\large{\frac{ \sqrt{s(s-a)(s-b)(s-c)}}{s-a} = \frac{\sqrt{s-a} \sqrt{s(s-b)(s-c)}}{s-a} }\]
anonymous
  • anonymous
prove it using either l.h.s or r.h.s
mathslover
  • mathslover
Yeah I am using LHS only
anonymous
  • anonymous
okay.. :)
mathslover
  • mathslover
well I can write :; \(\large{\frac{\sqrt{s-a}}{s-a} }\) as \(\frac{1}{\large{\sqrt{s-a}}}\)
mathslover
  • mathslover
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 : \[\large{s\tan \frac{\alpha}{2}}\]
mathslover
  • mathslover
got it ?
anonymous
  • anonymous
can u prove it by multiplying and dividing trick i did'nt understand the roots u changed
anonymous
  • anonymous
like taking r.h.s and M & D it by \[\sqrt{s(s-a)}\]
mathslover
  • mathslover
see : |dw:1360917633731:dw|
anonymous
  • anonymous
NUMBER 2\[\frac{ s-a }{ \Delta }+\frac{ s-b }{ \Delta }+\frac{ s-c }{ \Delta }= \frac{ s }{ \Delta }\]
anonymous
  • anonymous
Using lhs
anonymous
  • anonymous
\[\frac{ s-a+s-b+s-c }{ \Delta }\]
anonymous
  • anonymous
what to do after this??
hartnn
  • hartnn
didn't you ask the first one earlier also? :O also, for 2nd, we know that s is the semi-perimeter , hence, \(s= (a+b+c)/2 ------> 2s = a+b+c\) so, your numerator\( = s-a+s-b+s-c = 3s- (a+b+c) =.... ?\)
anonymous
  • anonymous
:D yes i did asked the first 1

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