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Math Help - Double Angles

  1. #1
    Newbie
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    Nov 2008
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    Double Angles

    How would I simplify:

    (tan22.5)/1 - tan^2(22.5)

    And also:

    let csc t = (square root)5 with t in QII and find sec 2t

    I have no idea where to start
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  2. #2
    Newbie Arch_Stanton's Avatar
    Joined
    Nov 2008
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    =\frac{\frac{sin x}{cos x}}{1-\frac{sin^2 x}{cos^2 x}}=...=\frac{sin x cos x}{cos^2 x-sin^2 x}=\frac{2sin x cos x}{2(cos^2 x-sin^2 x)}=\frac{sin2x}{2cos2x}=\frac{sin 45^o}{2cos 45^o}=\frac{1}{2}

    2. sec=\frac{1}{cos x}
    csc x=\frac{1}{sin x}
    csc t=\sqrt{5} \Rightarrow sin t=\frac{\sqrt{5}}{5}
    from the pythagorean trigonometric identity:
    sin^2 x+cos^2 x=1
    cos t=\sqrt{1-\frac{5}{25}}=\frac{2}{\sqrt{5}}
    cos 2t=cos^2 t-sin^2 t=\frac{4}{5}-\frac{1}{5}=\frac{3}{5}
    sec 2t=\frac{1}{cos 2t}=\frac{5}{3}
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