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neeraj_agarwal_1990 (887)

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Evaluate:
[n][infinity] { 1/2(tan x/2) +  1/22 (tan x/22) + 1/23(tan x/23).......1/2n(tan x/2n)}

[ans: 1/x - cotx]
    
rajat (284)

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i dunno the answer to dis deadly question ,but tell me ,is it objective ??

light travels the fastest ??? NO
wherever light goes it always finds that darkness has already got there
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neeraj_agarwal_1990 (887)

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no its not objective...
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uday_zingtudor (931)

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[n][infinity] { 1/2(tan x/2) +  1/22 (tan x/22) + 1/23(tan x/23).......1/2n(tan x/2n)}
 
Adding and subtracting 1/2ncotx/2n
 
Now,
 
We know that cotx-tanx=2cot2x
 
Here,
           - 1/2ncotx/2n+1/2ntanx/2n = -1/2n-1cotx/2n-1
 
Doing thus all the way in the problem, we get left with
 
 
[ n][infinity ] - cotx +1/2ncotx/2n
 
= - cotx +[ n][ infinity] 1/2ncotx/2n
 
= - cotx + 1/x { On applying the limits}
 
= 1/x - cotx
 
~Cheerio!!!!!

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don't get scared !!!
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neeraj_agarwal_1990 (887)

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How did u solve that uday??
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uday_zingtudor (931)

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i'm editing the post

Talk less work more!! {To be simplistic and 2 gain respect}

Eat less work more!!! {To "build" ur body}

Work less Do more!!! {2 make ur life big}












don't get scared !!!
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neeraj_agarwal_1990 (887)

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Got it man..
I just dont realise when to use that identity cotx-tanx=2cot2x
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sudeep.kumar (611)

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Well done Uday.

Sudeep Kumar
(B tech, IITd)

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