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Math Help - t formulae

  1. #1
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    t formulae

    Hi All,

    Having a shocker with this one aswell.

    If x = tan theta + sec theta, use the t formulae to show that (x^2 - 1) / (x^2 + 1) = sin theta

    I am lost with one. Thanks
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  2. #2
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    Quote Originally Posted by Joel View Post
    Hi All,

    Having a shocker with this one aswell.

    If x = tan theta + sec theta, use the t formulae to show that (x^2 - 1) / (x^2 + 1) = sin theta

    I am lost with one. Thanks

    And you think the whole world knows what the "t formulae" is? Same things can be taught very differently in different parts of the world...

    x=\tan \theta+\sec \theta\Longrightarrow x=\frac{\sin \theta+1}{\cos \theta} , so:

    \frac{x^2-1}{x^2+1}=\frac{\frac{\sin^2\theta+2\sin \theta+1}{\cos^2\theta} -1}{\frac{\sin^2 \theta+2\sin \theta+1}{\cos^2 \theta}+1}=\frac{\sin^2\theta+2\sin \theta+1-\cos^2\theta}{\sin^2\theta+2\sin \theta+1+\cos^2\theta} =\frac{2\sin^2\theta+2\sin \theta}{2+2\sin \theta}=\sin \theta

    Tonio
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