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Math Help - Trigonometric Identities

  1. #1
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    Trigonometric Identities

    Prove the identity tan 2x - tan x = tan x sec 2x

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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by BeckyDWood View Post
    Prove the identity tan 2x - tan x = tan x sec 2x

    Thank you for your time and help

    \tan 2x -\tan x = \tan x \sec 2x


    take the left side

    \tan 2x - \tan x = \frac{\sin 2x }{\cos 2x} - \frac{\sin x }{\cos x}

    \tan 2x - \tan x = \frac{\sin 2x \cos x - \sin x \cos 2x }{\cos 2x \cos x}

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

    \tan 2x - \tan x = \frac{\sin x( 2\cos ^2 x - \cos 2x }{\cos 2x \cos x}

    \tan 2x - \tan x = \frac{\sin x }{\cos 2x \cos x } =\tan x \sec 2x
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by Amer View Post
    \tan 2x - \tan x = \frac{\sin 2x \cos x - \sin x \cos 2x }{\cos 2x \cos x}
    note that \sin 2x \cos x - \sin x \cos 2x=\sin(2x-x)=\sin x.
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