## koli123able 2 years ago Prove the followings

1. koli123able

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

2. mathslover

what does alpha , a , s , $$\Delta$$ represent ?

3. koli123able

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

4. koli123able

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

5. mathslover

right... got it now..

6. mathslover

so now put these values : $\large{\frac{ \sqrt{s(s-a)(s-b)(s-c)}}{s-a} = \frac{\sqrt{s-a} \sqrt{s(s-b)(s-c)}}{s-a} }$

7. koli123able

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

8. mathslover

Yeah I am using LHS only

9. koli123able

okay.. :)

10. mathslover

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

11. 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 : $\large{s\tan \frac{\alpha}{2}}$

12. mathslover

got it ?

13. koli123able

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

14. koli123able

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

15. mathslover

see : |dw:1360917633731:dw|

16. koli123able

NUMBER 2$\frac{ s-a }{ \Delta }+\frac{ s-b }{ \Delta }+\frac{ s-c }{ \Delta }= \frac{ s }{ \Delta }$

17. koli123able

Using lhs

18. koli123able

$\frac{ s-a+s-b+s-c }{ \Delta }$

19. koli123able

what to do after this??

20. 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$$= s-a+s-b+s-c = 3s- (a+b+c) =.... ?$$

21. koli123able

:D yes i did asked the first 1