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Math Help - Trigonometic Identities

  1. #1
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    Trigonometic Identities

    Hi there .. I'm not sure how to approach this question and I would greatly appreciate it if someone could help me

    Thanks a bunch .

    Here's the question :

    Prove the identity .

    sin^4x - cos^4x = sin^2x - cos^2x
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  2. #2
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    Quote Originally Posted by asiankatt View Post
    Hi there .. I'm not sure how to approach this question and I would greatly appreciate it if someone could help me

    Thanks a bunch .

    Here's the question :

    Prove the identity .

    sin^4x - cos^4x = sin^2x - cos^2x
    This is very simple.
    Factor the left hand side,
    x^4-y^4=(x^2-y^2)(x^2+y^2)
    Thus,
    (\sin^2 x+\cos^2 x)(\sin^2 x-\cos^2 x)
    But,
    \sin^2 x+\cos^2 x=1
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  3. #3
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    =)

    Thanks a lot =) Now that I look at it .. it is really simple :S


    .... I have another question if you dont mind answering it ...


    Prove the indentity .

    4/cos^2x - 5 = 4tan^2 x - 1
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  4. #4
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    Quote Originally Posted by asiankatt View Post
    Thanks a lot =) Now that I look at it .. it is really simple :S


    .... I have another question if you dont mind answering it ...


    Prove the indentity .

    4/cos^2x - 5 = 4tan^2 x - 1
    Express left hand side as,
    \frac{4}{\cos^2 x}-4-1
    Factor, and use reciprocal identity,
    4(\sec^2 x-1)-1
    But,
    \tan^2 x+1=\sec^2 x
    Thus,
    4\tan^2 x-1
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