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Math Help - Verifying Trig Identities?

  1. #1
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    Verifying Trig Identities?

    Hello there.

    I am having some trouble in studying verifying trig identities for my Math final.


    ____1____ + _____1____ = 2Sec^2x
    1-Sinx 1+Sinx


    It's 1 over 1-Sinx plus 1 over 1 plus Sinx, equals 2 Sec squared x. I can't figure this one out. I think you have to get a common denominator, but I'm not sure, what to do after that.

    1-Sinx
    _________ = Sec^2x - 2secxtanx+tan^2x

    1+Sinx

    For this one, you work almost exclusively on the right side, no? I got (Secx-tanx)(Secx-tanx).

    From there don't you use reciprocal identities? After that, I am stuck.

    Any help would be appreciated. Also, since I am positive these will be on my final, can anyone give me general help/tips on solving these? A link to a good site would be very helpful. Thanks in advance.
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  2. #2
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    Quote Originally Posted by Quasimoto View Post
    Hello there.

    I am having some trouble in studying verifying trig identities for my Math final.


    ____1____ + _____1____ = 2Sec^2x
    1-Sinx 1+Sinx


    It's 1 over 1-Sinx plus 1 over 1 plus Sinx, equals 2 Sec squared x. I can't figure this one out. I think you have to get a common denominator, but I'm not sure, what to do after that.

    1-Sinx
    _________ = Sec^2x - 2secxtanx+tan^2x

    1+Sinx

    For this one, you work almost exclusively on the right side, no? I got (Secx-tanx)(Secx-tanx).

    From there don't you use reciprocal identities? After that, I am stuck.

    Any help would be appreciated. Also, since I am positive these will be on my final, can anyone give me general help/tips on solving these? A link to a good site would be very helpful. Thanks in advance.
    Dear Quasimoto,

    For the first one, get the common denominator as suggested. Then you should know that,

    sin^{2}x+cos^{2}x=1\Rightarrow{cos^{2}x=1-sin^{2}x}

    The second part could also be solved using the above identity.

    Hope you can continue.
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