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Thread: 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

    $\displaystyle 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

    $\displaystyle \frac{cos^2t-sin^2t}{cos^2t} = 1- \frac{sin^2t}{cos^2t}$
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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: .$\displaystyle \tan x \:=\: \frac{\sin 2x}{1+ \cos 2x} $
    You need to know some Double-angle identities:

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

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


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

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