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Math Help - Help with proofs

  1. #1
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    Help with proofs

    ᴓ=pheta

    1. (sinᴓ + cosᴓ)² = 1+sin2ᴓ

    2.cot2ᴓ=cos²ᴓ-sin²ᴓ over 2sinᴓ cosᴓ

    3.tan2ᴓ=2 over cotᴓ-tanᴓ
    Last edited by TJ123456; May 3rd 2009 at 04:57 PM.
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  2. #2
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    can someone please help?
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  3. #3
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by TJ123456 View Post
    ᴓ=pheta

    1. (sinᴓ + cosᴓ)² = 1+sin²ᴓ

    2.cotᴓ=cos²ᴓ-sin²ᴓ over 2sinᴓ cosᴓ

    3.tan2ᴓ=2 over cotᴓ-tanᴓ
    1. Expand like you would any other function:

    sin^2(\theta) + 2sin(\theta)cos(\theta) + cos^2(\theta) = 1+ 2sin(\theta)

    It would appear number 1 is not an identity. (try 90deg)

    2. cot(\theta) = \frac{cos^2(\theta)-sin^2(\theta)}{2sin(\theta)cos(\theta)} = \frac{cos(2\theta)}{sin(2\theta)} = cot(2(\theta))

    2 is not an identity either (try 45 degrees)

    3. \frac{2}{cot(\theta)-tan(\theta)} = \frac{2}{\frac{cos^2(\theta)-sin^2(\theta)}{cos(\theta)sin(\theta)}}

    Looking at the denominator: cos(\theta)sin(\theta) = \frac{1}{2}sin(2\theta)

    \frac{cos^2(\theta)-sin^2(\theta)}{cos(\theta)sin(\theta)} = \frac{2cos(2\theta)}{sin(2\theta} = 2cot(2\theta)

    The original expression becomes: \frac{2}{2cot(2\theta)} = tan(2\theta)
    Last edited by e^(i*pi); May 3rd 2009 at 05:08 PM. Reason: misread a minus sign
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  4. #4
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    thanks,my teacher said they would all work,so i went back and check my typing(i was in hurry this morning) and i did made a typo,so thats why they didnt work,i edit them just now if u wanna help again but you dont have too,again thanks man
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