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Math Help - Simplifying expressions

  1. #1
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    Simplifying expressions

    1)Tan0 + Cot0

    2)1-Sec(2)0
    ------------
    1-Cosec(2)0

    3) Sin0
    ----------
    Cosec0 - Cot0

    4) 1+Cos2 0


    0 = 0 with a line through the middle, not sure how you do it on the forums, and anything in brackets is power of.

    Any help with this would be appreciated.

    thank you!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Kim2425 View Post
    1)Tan0 + Cot0
    Let's call "0" = t for convenience.

    tan(t) + cot(t) = sin(t)/cos(t) + cos(t)/sin(t) <-- Get a common denominator then add the fractions:

    = [sin^2(t) + cos^2(t)]/[sin(t)cos(t)]

    = 1/[sin(t)cos(t)]

    We can work with this a bit more:

    = 2/[2sin(t)cos(t)] = 2/sin(2t) = 2*csc(2t)

    -Dan

    TECHNICAL COMMENT: Tan(t) and tan(t) are technically two different functions. The correct usage for the common trig functions is sin(t), cos(t), tan(t), csc(t), sec(t), and cot(t).
    Last edited by topsquark; March 27th 2007 at 06:58 PM.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Kim2425 View Post
    2)1-Sec^2(t)
    ------------
    1-csc^2(t)
    First note that:
    1 - sec^2(t) = tan^2(t)
    and
    1 - csc^2(t) = cot^2(t)

    So:
    [1 - sec^2(t)]/[1 - csc^2(t)] = tan^2(t)/cot^2(t) = tan^4(t)

    -Dan
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Kim2425 View Post
    3) Sin(t)
    ----------
    Csc(t) - Cot(t)
    sin(t)/[csc(t) - cot(t)] = sin(t)/[1/sin(t) - cos(t)/sin(t)]

    Multiply the numerator and denominator of the overall fraction by sin(t):

    sin^2(t)/[1 - cos(t)] (We need to keep in the back of our minds that sin(t) cannot be 0 from here on, but it couldn't do that in the original expression anyway.)

    Multiply the numerator and denominator by 1 + cos(t):

    [sin^2(t)*(1 + cos(t))]/[1 - cos^2(t)] = [sin^2(t)*(1 + cos(t))]/[sin^2(t)]

    = 1 + cos(t)

    -Dan
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Kim2425 View Post
    4) 1+Cos^2(t)
    Is there a typo in here? I can't think of anything to do with this one.

    -Dan
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