Prove the followings

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Prove the followings

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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