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Math Help - Making A Trig Identity

  1. #1
    Junior Member
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    Making A Trig Identity

    Ok so I have to make up a trig identity

    The instructions are to start with a statement that I know is true, and than keep changing both sides to equivalent equations until it is complex

    So far I have:

    cos²x = cos²x

    1-sin²x = cos2x + sin²x

    I need 2 more lines of changing them until the final identity..

    But I don't know how to keep going!

    Any help?



    Thanks
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  2. #2
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    Hello, advancedfunctions2010!

    Exactly what are the directions?


    Ok, so I have to make up a trig identity

    The instructions are to start with a statement that I know is true,
    and then keep changing both sides to equivalent equations until it is complex.


    So far I have: . \cos^2\!x \:=\:\cos^2\!x

    . . . . . . 1-\sin^2\!x \:=\: \cos2x + \sin^2\!x

    I need 2 more lines of changing . . . . Why two more lines?

    How about: . 1-\sin^2\!x \;=\;\cos^2\!x

    . . . (1-\sin x)(1 + \sin x) \;=\;\cos^2\!x

    . . . . . . . . . \frac{1-\sin x}{\cos x} \;=\;\frac{\cos x}{1 + \sin x}


    Another: . (\sin x + \cos x)^2 \;=\;(\sin x + \cos x)^2

    . . . . . . . (\sin x + \cos x)^2 \;=\;\sin^2\!x + 2\sin x\cos x + \cos^2\!x

    . . . . . . . (\sin x + \cos x)^2 \;=\;\underbrace{\sin^2\!x + \cos^2\!x}_{\text{This is 1}} + \underbrace{2\sin x\cos x}_{\text{This is }\sin2x}

    . . . . . . . (\sin x + \cos x)^2 \;=\;1 + \sin2x

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  3. #3
    Junior Member
    Joined
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    The exact instructions are:

    Start with a statement you know is true for all values of x; for example sin²x = sin²x

    Progressively change each side into an equivalent, but more complex form; for example 1 - cos²x = -cos2x + cos²x

    Continue replacing terms with equivalent expressions until you decide that your identity is sufficiently complex
    ( min. 3 lines of changing before the final identity )


    So pretty much just have to keep changing them.. but my problem was running out of things to change into lol





    is all i could go.. i didn't know how to change them any further

    thanks so much for helping!
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