IIT JEE , AIEEE Forum - Mathematics , Trignometry

ramkumar_november

The proof is ......
We know that cot (A+B)= (1-cotAcotB)/(cotA+cotB)
or cotAcotB=1- [cot(A+B)*(cotA+cotB)].............(i)

similarly cotAcotB=[cot(A-B)*(cotB-cotA)] - 1............(ii)

putting A=16 and B=44 in (i) we get
cot16cot44 = 1-[cot60*(cot16+cot44)]......(iii)

putting A=44 and B=76 in (i) we get
cot44cot76 = 1 - [cot120*(cot76+cot44)]
cot44cot76 = 1 +[cot60*(cot76+cot44)]..............(iv)
(since cot120 = -cot60)

putting A=16 and B=76 in (ii) we get
cot76cot16 = [cot60*(cot76-cot16)] -1............(v)

(iii) + (iv) - (v) we get
cot16cot44 + cot44cot76 - cot76cot16 =
1 - cot60cot16 - cot60cot44 + 1 + cot60cot76 + cot60cot44 + 1
+ cot60cot16 - cot60cot76

on cancelling the terms we get........

cot16cot44 + cot44cot76 - cot76cot16 = 3

rahul .... ok with my proof?

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