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Math Help - Simplify trig equation

  1. #1
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    Simplify trig equation

    How do I simply (1+tan^2A)(1-sin^2A)
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello,
    Quote Originally Posted by zapparage View Post
    How do I simply (1+tan^2A)(1-sin^2A)
    You can start by using 1+\tan^2A=\frac{1}{\cos^2A}. If you're not supposed to know this identity you can start as follows :

    <br />
(1+\tan^2A)(1-\sin^2A)=(1+\tan^2A)\cos^2A=\left(1+\frac{\sin^2A}  {\cos^2A}\right)\cos^2A=\ldots
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  3. #3
    Super Member 11rdc11's Avatar
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    It Equals 1, it may take me a lil while to post the answer since I'm trying to learn latex lol.
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  4. #4
    Super Member 11rdc11's Avatar
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    {1-sin^2A} = cos^2A
    Last edited by 11rdc11; August 26th 2008 at 11:17 AM. Reason: oops was to late
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  5. #5
    Super Member 11rdc11's Avatar
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    Here is another way you could do it,

    1- sin^2A +tan^2A-tan^2Asin^2A= 1 -sin^2A +\frac{sin^2A}{cos^2A} -\frac{sin^4A}{cos^2A}


    \frac{cos^2A-sin^2Acos^2A+sin^2A-sin^4A}{cos^2A}


    \frac{cos^2A(1-sin^2A)+sin^2A(1-sin^2A)}{cos^2A}


    \frac{cos^4A+sin^2Acos^2A}{cos^2A}


    \frac {cos^2A(cos^2A + sin^2A)}{cos^2A}


    cos^2A + sin^2A= 1
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