If a,b,c are positives such that a+b+c=\frac{\pi}{2} and \cot(a),\cot(b),\cot(c) is

Miguel Davenport 2022-01-24 Answered
If a,b,c are positives such that a+b+c=π2 and cot(a),cot(b),cot(c) is in arithmetic progression, find cot(a)cot(c)
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Dakota Cunningham
Answered 2022-01-25 Author has 9 answers
As
cot(x+y)=cotxcoty1cotx+coty
cot(a+c)=cot(π2b)=tanb=1cotb=cotacotc1cota+cotc
1cotb=cotacotc12cotb
So,
cotacotc=1+2=3
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sjkuzy5
Answered 2022-01-26 Author has 11 answers
Write A=2a etc.
cotA2=s(sa)(sb)(sc)=s(sa)
We have sa+sc=2(sb)
a+c=2b2s=a+b+c=3b
cotA2cotC2=ssb=3  as  3b=2s
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