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Math Help - help with some questions

  1. #1
    Junior Member
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    help with some questions

    I am having trouble with some of these questions:

    1. 2 tan (5pi/8) = tan 5pi/4 (use the double angle formula, but what is the answer)?

    And ...

    2. Express tan in terms of cosine and sine.

    Do I use the Pythagorean identity? (1 + tan^2x = sec^2x and 1 + cot^2x = cot^2x)
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    1) The equality is wrong.

    \tan 2x=\frac{2\tan x}{1-\tan^2x}

    Then
    \tan\frac{5\pi}{4}=\tan\left(2\cdot\frac{5\pi}{8}\  right)=\frac{2\tan\frac{5\pi}{8}}{1-\tan^2\frac{5\pi}{8}}


    2)
    \tan x=\frac{\sin x}{\cos x}=\pm\frac{\sqrt{1-\cos^2x}}{\cos x}

    \tan x=\frac{\sin x}{\cos x}=\pm\frac{\sin x}{\sqrt{1-\sin^2x}}
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