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Math Help - Trig. Identity help please!

  1. #1
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    Trig. Identity help please!

    Im trying to study for my math 109/110 course in college
    and trig. id's are giving me the hardest problems

    we've learned about the identities for sin, cos, tan and excluding cot csc sec

    Prove the identity

    tan x =\frac{sin 2x}{1+ cos 2x}

    also how is this and identity the x values are not the same at all I thought that what trig. identity means for every x value both have the same output

    Also

    how is

    \frac{cos^2t-sin^2t}{cos^2t} = 1- \frac{sin^2t}{cos^2t}
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  2. #2
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    Smile

    Trig. Identity help please!-untitled.jpg
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  3. #3
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    Um ok?
    Care to explain?
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  4. #4
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    Hello, sk8erboyla2004!

    Prove the identity: . \tan x \:=\: \frac{\sin 2x}{1+ \cos 2x}
    You need to know some Double-angle identities:

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

    . . \cos^2\!\theta \:=\:\frac{1 + \cos2\theta}{2} \quad\Rightarrow\quad 1 + \cos2\theta \:=\:2\cos^2\!\theta


    Then: . \frac{\sin2x}{1+\cos2x} \;=\;\frac{2\sin x\cos x}{2\cos^2\!x} \;=\;\frac{\sin x}{\cos x} \;=\;\tan x

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