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Math Help - Proving identities

  1. #1
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    Proving identities

    2tanA / 1+tan2A = sin2A

    I know that 2tanA is tan a + tan a and that sin2A is 2sinAcosA

    Could someone help me figure out the rest?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Proving identities

    Traditionally, when proving identities you want to begin with one side (usually the left) and apply known standard identities and perhaps some algebra so that the right side results. Looking at the left side, I suggest you begin with the Pythagorean identity 1+\tan^2\theta=\sec^2\theta.
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  3. #3
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    Re: Proving identities

    Hi

    \\\mathrm{\tan(x+y)=\dfrac{\tan x+\tan y}{1-\tan x\tan y}}\\\mathrm{\tan(2A)=\dfrac{2\tan A}{1-\tan^2A}}\\\mathrm{\dfrac{\sin2A}{\cos2A}=\dfrac{2  \tan A}{1-\tan^2A}}\\\mathrm{\sin2A=\cos2A\times\dfrac{2\tan A}{1-\tan^2A}}\\\mathrm{\sin2A=\dfrac{\cos^2A-\sin^2A}{\cos^2A+\sin^2A}\times\dfrac{2\tan A}{1-\tan^2A}}\\\mathrm{\sin2A=\dfrac{1-\tan^2A}{1+\tan^2A}\times\dfrac{2\tan A}{1-\tan^2A}}\\\mathrm{\sin2A=\dfrac{2\tan A}{1+\tan^2 A}}

    Greetings
    Last edited by darthjavier; November 12th 2012 at 08:19 PM. Reason: learning how to type well with latex :p
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