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Math Help - Trigonometric Equations

  1. #1
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    Trigonometric Equations

    The equation is:  3 tan 2x - 4 = 6
    and I can get this equation down to \frac{6tanx}{(3-3tan^2x)} = \frac{10-tan^2x}{3-3tan^2x} but no further.

    the other problem is i can't prove the identity: \frac{sin2x + sin6x}{sin10x - sin2x} = \frac{cos2x}{cos6x} but i don't even know where to start

    I am starting to panic as this is a take home test due tomorrow and I am really getting stuck. Thanks a lot!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by qwerty723519@hotmail.com View Post
    The equation is:  3 tan 2x - 4 = 6
    and I can get this equation down to \frac{6tanx}{(3-3tan^2x)} = \frac{10-tan^2x}{3-3tan^2x} but no further.

    the other problem is i can't prove the identity: \frac{sin2x + sin6x}{sin10x - sin2x} = \frac{cos2x}{cos6x} but i don't even know where to start

    I am starting to panic as this is a take home test due tomorrow and I am really getting stuck. Thanks a lot!
    3\tan(2x)-4=6\Rightarrow{3\tan(2x)=10}

    Dividing we get \tan(2x)=\frac{10}{3}

    Taking the arctan of both sides we get

    2x=arctan\bigg(\frac{10}{3}\bigg)\Rightarrow{x=\fr  ac{\arctan\bigg(\frac{10}{3}\bigg)}{2}}
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by qwerty723519@hotmail.com View Post
    The equation is:  3 tan 2x - 4 = 6
    and I can get this equation down to \frac{6tanx}{(3-3tan^2x)} = \frac{10-tan^2x}{3-3tan^2x} but no further.

    the other problem is i can't prove the identity: \frac{sin2x + sin6x}{sin10x - sin2x} = \frac{cos2x}{cos6x} but i don't even know where to start

    I am starting to panic as this is a take home test due tomorrow and I am really getting stuck. Thanks a lot!
    For the second one try here

    Prosthaphaeresis Formulas -- from Wolfram MathWorld
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  4. #4
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    Thanks, I guess the first doesn't work out nicely. Regarding the second, I actually used those formulas for several of the other problems I had to do, but was unsure how to apply them in this case
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