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Thread: Trig proof - how do I prove this?

  1. #1
    Don
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    Trig proof - how do I prove this?

    Prove that

    $\displaystyle tan 4 theta = 4 tan theta (1-tan^2 theta)/1-6tan^2 theta + tan ^4 theta$

    (Sorry about that. I don't know how to use LaTEX, it's all messed up. I used the MATH tag and it showed an error and so I used the TEX tag).

    I don't know where to start. What trig identities should I use?
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  2. #2
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    Re: Trig proof - how do I prove this?

    Online LaTeX Equation Editor - create, integrate and download it's easier.

    $\displaystyle \tan(4\theta )=\frac{4\tan(\theta) (1-\tan^{2}(\theta))}{1-6\tan^2(\theta)+\tan^4(\theta)}$

    Use twice $\displaystyle \tan(2\theta )=\frac{2\tan(\theta)}{1-\tan^2(\theta)}$.
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  3. #3
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    Re: Trig proof - how do I prove this?

    Quote Originally Posted by Don View Post
    Prove that

    $\displaystyle \tan 4 \theta = 4 \tan \theta (1-\tan^2 \theta)/(1-6\tan^2 \theta + \tan ^4 \theta)$

    (Sorry about that. I don't know how to use LaTEX, it's all messed up. I used the MATH tag and it showed an error and so I used the TEX tag).

    I don't know where to start. What trig identities should I use?
    (Use the TEX tags, but put a backslash before each tan and each theta.)

    Use the formula $\displaystyle \tan(2\theta) = \frac{2\tan\theta}{1-\tan^2\theta}.$ Then use the same formula again to get $\displaystyle \tan(4\theta)$ in terms of $\displaystyle \tan(2\theta).$ Finally, combine the two formulas to get $\displaystyle \tan(4\theta)$ in terms of $\displaystyle \tan\theta.$
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  4. #4
    Don
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    Re: Trig proof - how do I prove this?

    Got it, thanks.
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