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   Author  Topic: simplify  (Read 2462 times)
tony123
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simplify  
« on: Nov 19th, 2007, 1:22pm »		 Quote Quote Modify Modify
simplify
 
tan1/cos2 +tan 2/cos 4+ tan 4/cos8+...+tan128/cos256
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Aryabhatta
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Re: simplify  
« Reply #1 on: Nov 19th, 2007, 4:04pm »		 Quote Quote Modify Modify
Cute problem.
 

Prove the identity tan 2x - tan x = tanx/cos2x
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thinktank
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Posts: 10
Re: simplify  
« Reply #2 on: Nov 19th, 2007, 7:05pm »		 Quote Quote Modify Modify
The above solution is right...actually this didnt come to my mind so I added
hidden:
tanx/cos2x +tan2x/cos4x
to get
hidden:
tan4x-tanx
...so on addition the result is
hidden:
tan 256-tan1
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cool_joh
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Re: simplify  
« Reply #3 on: Nov 24th, 2007, 7:04pm »		 Quote Quote Modify Modify Remove Remove
on Nov 19th, 2007, 4:04pm, Aryabhatta wrote:

Prove the identity tan 2x - tan x = tanx/cos2x

tan 2x - tan x = 2tanx/(1-tan2x) - tan x = (2tanx - (tan x - tan3x)) / (1-tan2x) = (tan x + tan3x) / (1-tan2x) = tan x * (1+tan2x)/(1-tan2x) = tan x / cos 2x
QED
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