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Trignometry

Scorching goIITian

 Joined: 18 Feb 2012 Post: 264
5 May 2012 15:13:21 IST
1 People liked this
3
314
again its me.
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Trigonometry

cot^2a+cot^2b+cot^2c=1. then ABC is wat triangle?

Blazing goIITian

Joined: 1 Apr 2007
Posts: 4025
6 May 2012 12:40:12 IST
0 people liked this

it can be any triangleit's an identity when a,b,c represents the angles of the triangle

New kid on the Block

Joined: 6 May 2012
Posts: 12
6 May 2012 12:42:05 IST
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@vikram saxena...it can only be equilateralll......ur answer is wrong.......standard of experts is very low here

Blazing goIITian

Joined: 19 Jan 2008
Posts: 1142
6 May 2012 14:16:12 IST
1 people liked this

$\hspace{-16}\bf{\cot^2(A)+\cot^2(B)+cot^2(C)=1}\\\\\\ \bf{2\cot^2(A)+2\cot^2(B)+2cot^2(C)=2}\\\\\\ \bf{\sum_{cyclic\;A,B,C}\cot^2(A)+\cot^2(B)-2\cot(A).\cot(B)=0}\\\\\\ Using If \bf{A+B+C=\pi}\\\\\\ Then \bf{\sum_{cyclic A,B,C}\cot(A).\cot(B)=1}\\\\\\ \bf{\sum_{cyclic\;A,B,C}\left(\cot(A)-\cot(B)\right)^2=0}\\\\\\ So \bf{\cot(A)=\cot(B)=\cot(C)=0}\\\\\\ So \bf{A=B=C}$

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