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Math Help - trig verifying identities

  1. #1
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    trig verifying identities

    I'd really appreciate it if someone could help me with these 2 problems!

    1) Verify the identity:

    Cosx/(1-sinx) = (1+sinx)/Cosx

    2) Simplify and express without fractions:

    (1-sin^2x)/(cot^2x+1)
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by angelkat007 View Post
    I'd really appreciate it if someone could help me with these 2 problems!

    1) Verify the identity:

    Cosx/(1-sinx) = (1+sinx)/Cosx

    2) Simplify and express without fractions:

    (1-sin^2x)/(cot^2x+1)
    For the second one use the identities 1-\sin^2(x)=\cos^2(x)
    and \csc^2(x)=1+\cot^2(x)

    as for the first one I would suggest multiplying both sides by cos(x)
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  3. #3
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    I think I screwed it up..so nevermind..go with what the genius mathstud says!!
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by elizsimca View Post
    2.

    \frac{1-\sin^2{x}}{\cot^2{x}+1} = (1-\sin^2{x})(\tan^2{x}+1) = (\cos^2{x})(\sec^2{x}) = \frac{\cos^2{x}}{\cos^2{x}} = 1

    I think..confirmation anyone?

    EDIT

    I think it's wrong..

    Dang!
    Everything is right based off your first assumption..but unfortunately that assumption is wrong......its ok though! at least you saw it was wrong...we all make mistakes..me ESPECIALLY included...ask anyone...I probably should get the award for most typos/clerical errors
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  5. #5
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    Yeah, I realized shortly after....

    Forum 1 Elizsimca 0


    Oh, and mathstud, I like how you brought me down gently....

    "Everything is right based off your first assumption..but unfortunately that assumption is wrong.."...haha, made me laugh!!
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by elizsimca View Post
    Yeah, I realized shortly after....

    Forum 1 Elizsimca 0


    Oh, and mathstud, I like how you brought me down gently....

    "Everything is right based off your first assumption..but unfortunately that assumption is wrong.."...haha, made me laugh!!
    Haha...Tough Love Elizsimca...tough love...the key to growth

    You seem to be a neo-denizen of MHF....its part of the process...well...I am also a new-comer...I still catch flack all the time
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  7. #7
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    so would the 2nd one be (cos^2 x)(sin^2 x)???
    Thanks so much for your help!
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  8. #8
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by angelkat007 View Post
    so would the 2nd one be (cos^2 x)(sin^2 x)???
    Thanks so much for your help!
    ..yes...good job!
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  9. #9
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    Quote Originally Posted by angelkat007 View Post
    so would the 2nd one be (cos^2 x)(sin^2 x)???
    Thanks so much for your help!
    Yeah, that's the answer my ti-89 gave me
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  10. #10
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by elizsimca View Post
    Yeah, that's the answer my ti-89 gave me
    Ahh...the TI-89...the greatest thing ever...I ♥ my TI-89
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