|
|
|
|
|
| Author |
Message |
![[Post New]](/templates/default/images/icon_minipost_new.gif) 29 Jun 2007 21:05:06 IST
|
|
|
| tan(A+P) tan(B+P) tan(C+P) | | | | tan(A+Q) tan(B+Q) tan(C+Q) | | | | tan(A+R) tan(B+R) tan(C+R) | show that the value of the diterminant vanishes for all values of A,B,C,P,Q,R. Such that, A+B+C+P+Q+R=0.
|
Keep working....................Iam comming..
your's only,
Success!! |
|
|
|
29 Jun 2007 22:26:31 IST
|
|
|
A+B+C+P+Q+R = 0
Now do the following transformations
C1  C1+C2+ C3
And then,
R1 R1+R2+R3
R2 R1+R2+R3
R3 R1+R2+R3
All the first row elements become the same. You get the first row's elements as
tan(A+P)+tan(A+Q)+tan(A+R)+tan(B+P)+tan(B+Q)+tan(B+R)+tan(C+P)+tan(C+Q)+tan(C+R)
=tan(A+P +A+Q+A+R+B+P+B+Q+B+R+C+P+C+Q+C+R) x Dr of [tan(A+P +A+Q+A+R+B+P+B+Q+B+R+C+P+C+Q+C+R)]
= tan(3(A+B+C+P+Q+R)) x Dr of[tan(3(A+B+C+P+Q+R))]
= 0 x Dr of[tan(3(A+B+C+P+Q+R))]
= 0
Hence each of the first row elements become zero
Hence the determinant is zero for all values of A,B,C,P,Q,R.
|
|
this reply: 5 points
(with 1 
in 1 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
1 Jul 2007 14:21:55 IST
|
|
|
good work elessar_iitkgp
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
2 Jul 2007 15:37:22 IST
|
|
|
elessar sir,
how the 1st row elements become same?????
the element which is =0 is only 1st row 1st element...
|
Keep working....................Iam comming..
your's only,
Success!! |
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
|
|
|
|
|
|
|
Moderation Team
![[Up]](/templates/default/images/icon_up.gif "[Up]"){kind=icon}
