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[Post New]9 Jan 2007 09:32:55 IST
    Subject: Re:solve and get a salute
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puneet (3568)

Forum Expert Blazing goIITian

Olaaa!! Perrrfect answer. 620  bad job dude!! I dont approve of this answer! 2  [858 rates]
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total posts: 1966    
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well let us denote sum by  S
so S = tan2 /16 + tan2 2/16 + tan2 3/16 + tan2 4/16 + tan2 5/16 + tan2 6/16 + tan2 7/16 
        =  tan2 /16 + tan2 2/16 + tan2 3/16 + 1 + cot2 /16 + cot2 2/16 + cot2 3/16
           = (tan /16 - cot /16)2 + (tan 2/16 - cot 2/16)2 +  (tan 3/16 - cot 3/16)2 + 2 + 2 + 2 +1
    Now note that tanx - cotx = - 2 cot2x
so S = 4cot2 2/16 + 4cot2 4/16 + 4cot2 6/16 + 7
        = 4cot2 2/16 + 4 + 4cot2 6/16 + 7
        = 4 (cot2 2/16 + cot2 6/16) + 11
       = 4(cot2 2/16 + tan2 2/16) + 11
       = 4( (tan 2/16 - cot 2/16)2 + 2) + 11
     = 4(tan 2/16 - cot 2/16)2 + 8+ 11
      = 4 ( 4cot2 4/16) + 19
      = 4.4 + 19
      = 16 + 19
      = 35
 
so the answer is 35 .......... cheeeeers
 
Puneet Agrawal
IIT Delhi
 this reply: 20 points  (with 4 Olaaa!! Perrrfect answer.   in 4 votes )   [?]
 
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