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In triangle ABC prove that if alb, c are in AP then Cot(A/2), Cot(B/2), Cot (C/2) are in AP

In triangle ABC prove that if alb, c are in AP then Cot(A/2), Cot(B/2), Cot (C/2) are in AP

 

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
Let us assume that
CotA/2 , cot B/2, cotC/2  are in A.P.
 
s(s-a)/delta,  s(s-b)/delta,  s(s-c)/delta        ....A.P.
Multiply by delta/s
 
(s-a), (s-b), (s-c)       .......A.P.
Now
Subtract s
 
-a, -b, -c         .....A.P
Multiply by -1
 
a, b, c        A.P.
 
Hence proved
 
Regards
Arun (askIITians forum expert)
 

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