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Math Help - Double angle formula

  1. #1
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    Double angle formula

    Hi ya'll. Quick question

    using double angle formula, verify that

    csc(2theta) - cot (2theta) = tan theta

    im so very confused.

    Working would be helpful to thanks
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  2. #2
    Senior Member
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    Crna Gora
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    Re: Double angle formula

    Quote Originally Posted by Hooperoo View Post
    Hi ya'll. Quick question

    using double angle formula, verify that

    csc(2theta) - cot (2theta) = tan theta

    im so very confused.

    Working would be helpful to thanks
     \frac{1}{\sin 2\theta}-\frac{\cos 2\theta}{\sin 2\theta}=\frac{1-(cos^2 \theta-\sin^2 \theta)}{2\sin \theta \cdot \cos \theta}=

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

    =\frac{2\sin^2 \theta}{2\sin \theta \cdot \cos \theta}=\frac{\sin \theta}{\cos \theta}=\tan \theta
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  3. #3
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    Re: Double angle formula

    Dang. You make it seem so easy! I had an attempt at it, and i got kinda close. But thank you@!
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  4. #4
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    Lexington, MA (USA)
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    Re: Double angle formula

    Hello, Hooperoo!

    You are expected to know these identities:

    . . \sin2\theta \:=\:2\sin\theta\cos\theta

    . . \sin^2\!\theta \:=\:\frac{1-\cos2\theta}{2} \quad\Rightarrow\quad 1 - \cos2\theta \:=\:2\sin^2\!\theta


    Using double-angle formulas, verify that: . \csc2\theta - \cot2\theta \:=\:\tan\theta

    We have: . \csc2\theta - \cot2\theta \;=\;\frac{1}{\sin2\theta} - \frac{\cos2\theta}{\sin2\theta} \;=\;\frac{1 - \cos2\theta}{\sin2\theta}

    . . . . . . . . . . . . . . . . . . . \;=\;\frac{2\sin^2\!\theta}{2\sin\theta\cos\theta} \;=\;\frac{\sin\tjeta}{\cos\theta} \;=\;\tan\theta
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