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Math Forum » Discussions » Math Topics » alt.math.undergrad.independent

Topic: sin(2x)=tanx, can't find all solutions
Replies: 7   Last Post: Sep 22, 2006 2:02 AM

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Vijaya Prasad Nalluri

Posts: 8
From: India
Registered: 4/10/06
Re: sin(2x)=tanx, can't find all solutions
Posted: Sep 22, 2006 2:02 AM
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Denote tan x = t
Given equation can be written as 2t /(1+t^2) = t
t(1 + t^2 -2) = 0
t = 0 or t = 1 or t = -1
tan x = 0 or tan x = 1 or tan x = -1
x = n pi or x = n pi + (pi/4) or x = n pi - (pi/4)
where n 1s any integer.

Vijayaprasad

> I'm trying to solve sin(2x)=tanx, but I can't seem to
> find all the
> solutions. This is what I've got:
> sin2x=tanx
> 2sinxcosx=sinx/cosx
> cos^2x=1/2
> cosx=+-1/sqrt2
> x=+-pi/4+pi2k (k=0, +-1, +-2...)
> x=+-3pi/4+pi2k
> But there are more solutions than these, for example
> x=pi. How do I find
> them?
>
> /Johan

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