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        riddles >> medium >> simplify
        
(Message started by: tony123 on Nov 19th, 2007, 1:22pm)
Title: simplify
Post by tony123 on Nov 19th, 2007, 1:22pm
simplify

tan1/cos2 +tan 2/cos 4+ tan 4/cos8+...+tan128/cos256
Title: Re: simplify
Post by Aryabhatta on Nov 19th, 2007, 4:04pm
Cute problem.

[hide]
Prove the identity tan 2x - tan x = tanx/cos2x
[/hide]
Title: Re: simplify
Post by thinktank on Nov 19th, 2007, 7:05pm
The above solution is right...actually this didnt come to my mind so I added [hideb]tanx/cos2x +tan2x/cos4x[/hideb] to get [hideb]tan4x-tanx[/hideb]...so on addition the result is [hideb]tan 256-tan1[/hideb]
Title: Re: simplify
Post by cool_joh on Nov 24th, 2007, 7:04pm

on 11/19/07 at 16:04:41, Aryabhatta wrote:
[hide]
Prove the identity tan 2x - tan x = tanx/cos2x
[/hide]

[hide]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[/hide]


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