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Math Help - Trig proofs help!

  1. #1
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    Trig proofs help!

    Hi! I needed help verifying the following proofs! If anyone wants to contribute by solving either of them, I will greatly appreciate it!

    Sin^(4) x - cos^(4) x = 1-2cos^(2) x

    and:

    sec x - sin x • tan x = cos x

    and:

    {(cos^(2) x)/(1+ sin x)} -1= -sin x

    thank you!
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  2. #2
    Super Member bigwave's Avatar
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    (sin^2 - cos^2)(1) = sin^2 - cos^2

    here is the first one

    Sin^{4}x - cos^{4} x = 1-2cos^{2} x

    (sin^2 - cos^2)(sin^2 + cos^2) = sin^2 + cos^2 - 2cos^2

    <br />
(sin^2 - cos^2)(1) = sin^2 - cos^2

    continue more??
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  3. #3
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    Wow! Thank you so much! Yes, can you please show me the other ones?
    Also, can you try verifying them by only working on the left side of the equation? I have to do it that way sorry
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  4. #4
    Super Member bigwave's Avatar
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    the last 2

    sec x - sin x tan x = cos x

    get all terms in sinx and cosx

    \frac{1}{cosx} - sinx \frac{sinx}{cosx}  =  cosx

    \frac{1 - sin^{2}x}{cosx} = cosx

    \frac{cos^{2}x}{cosx} = cosx

    cosx = cosx

    --------------------------------------------------------

    \frac{cos^{2}x}{1 + sinx} - 1 = -sinx

    cos^{2}x = (-sin+1)(1+ sinx)

    or cos^{2}x = (1-sinx)(1+ sinx) = 1 - sin^{2}x

    cos^{2}x = cos^{2}x
    Last edited by bigwave; December 13th 2009 at 11:52 PM. Reason: added identity proof
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  5. #5
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    Quote Originally Posted by bigwave View Post
    sec x - sin x tan x = cos x

    get all terms in sinx and cosx

    \frac{1}{cosx} - sinx \frac{sinx}{cosx}  =  cosx

    \frac{1 - sin^{2}x}{cosx} = cosx

    \frac{cos^{2}x}{cosx} = cosx

    cosx = cosx
    wait a sec.... When you combined the left side to form (1-sin^2x)/(cosx) , aren't you also supposed to multiple the denominators? So would the correct combination be : (1-sin^2x)/(cos^2x) ?

    EDIT: nevermind, you're right whoops
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  6. #6
    Super Member bigwave's Avatar
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    we are adding 2 fractions not mulitplying
    the common denominator is cosx
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  7. #7
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    One laaaast thing
    can you complete the first one but this time only work on the left side? Thank you so much, you're very helpful
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  8. #8
    Super Member bigwave's Avatar
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    sin^{4}x - cos^{4}x = 1-2cos^{2}x

    (sin^{2}x - cos^{2}x)(sin^{2}x + cos^{2}x) = 1-2cos^{2}x

    <br />
((1-cos^{2}x) - cos^{2}x)(1) = 1-2cos^{2}x
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