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Math Help - Identities

  1. #1
    Junior Member
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    Identities

    Can anyone help me change [4cos^4(x/2)]/tan^2 x into cos^2 x/[tan^2(x/2)] ?

    Thanks.
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  2. #2
    MHF Contributor red_dog's Avatar
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    \tan x=\frac{2\tan\frac{x}{2}}{1-\tan^2\frac{x}{2}}

    Then \tan^2x=\frac{4\tan^2\frac{x}{2}}{\left(1-\tan^2\frac{x}{2}\right)^2}=4\tan^2\frac{x}{2}\cdo  t\frac{\cos^4\frac{x}{2}}{\cos^2x}

    \frac{4\cos^4\frac{x}{2}}{\tan^2x}=\frac{4\cos^4\f  rac{x}{2}}{4\tan^2\frac{x}{2}}\cdot\frac{\cos^2x}{  \cos^4\frac{x}{2}}=\frac{\cos^2x}{\tan^2\frac{x}{2  }}
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