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Prove the followings

Mathematics
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Number 1 \[\frac{ \Delta }{ s-a }=s \tan \frac{ \alpha }{ 2 }\]
what does alpha , a , s , \(\Delta\) represent ?
\[\Delta=\sqrt{s(s-a)(s-b)(s-c)}\]

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Other answers:

\[\tan \frac{ \alpha }{ 2 }=\sqrt{\frac{ (s-b)(s-c) }{ s(s-a) }}\]
right... got it now..
so now put these values : \[\large{\frac{ \sqrt{s(s-a)(s-b)(s-c)}}{s-a} = \frac{\sqrt{s-a} \sqrt{s(s-b)(s-c)}}{s-a} }\]
prove it using either l.h.s or r.h.s
Yeah I am using LHS only
okay.. :)
well I can write :; \(\large{\frac{\sqrt{s-a}}{s-a} }\) as \(\frac{1}{\large{\sqrt{s-a}}}\)
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 : \[\large{s\tan \frac{\alpha}{2}}\]
got it ?
can u prove it by multiplying and dividing trick i did'nt understand the roots u changed
like taking r.h.s and M & D it by \[\sqrt{s(s-a)}\]
see : |dw:1360917633731:dw|
NUMBER 2\[\frac{ s-a }{ \Delta }+\frac{ s-b }{ \Delta }+\frac{ s-c }{ \Delta }= \frac{ s }{ \Delta }\]
Using lhs
\[\frac{ s-a+s-b+s-c }{ \Delta }\]
what to do after this??
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\( = s-a+s-b+s-c = 3s- (a+b+c) =.... ?\)
:D yes i did asked the first 1

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