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Math Help - Verifying identities

  1. #1
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    Exclamation Verifying identities

    I'm a little confused how to start this problem:

    1 + cosx + sinx
    sinx 1 + cosx
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  2. #2
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    Quote Originally Posted by Lauren Schmidt View Post
    I'm a little confused how to start this problem:

    1 + cosx + sinx
    sinx 1 + cosx
    Lauren you have to be a little more clear on your problem. Are we proving this identity to be something else? It just looks like a whole lot of cos's and sin's thrown onto the screen at the moment.

    Could it be like this?

    \frac{1+cos(x)+sin(x)}{sin(1+cos(x))} = \cdots
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  3. #3
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    oh goodness. haha. i'm sorry. it's = to 2 cscx


    1 + cosx + sinx = 2 cscx
    sinx 1 + cosx
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  4. #4
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    Quote Originally Posted by Lauren Schmidt View Post
    oh goodness. haha. i'm sorry. it's = to 2 cscx


    1 + cosx + sinx = 2 cscx
    sinx 1 + cosx
    So maybe?

    \frac{1+cos(x)+sin(x)}{sin(1+cos(x))} = 2 cosec(x)
    Last edited by pickslides; April 22nd 2009 at 04:58 PM. Reason: Typo
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  5. #5
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    Looks like a tricky one, these proofs can be unforgiving at times but if you get one to fall out it feels great.


    Have a look at this list of identities

    Table of Trigonometric Identities

    Then remember that

    \frac{1}{sin(x)} = cosec(x)

    Try try to put everything one the left hand side in terms of sin(x)
    Last edited by pickslides; April 22nd 2009 at 05:07 PM. Reason: Typo
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  6. #6
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    Quote Originally Posted by Lauren Schmidt View Post
    oh goodness. haha. i'm sorry. it's = to 2 cscx


    1 + cosx + sinx = 2 cscx
    sinx 1 + cosx
    please use grouping symbols to make your post clear ...

    (1+cosx)/sinx + sinx/(1+cosx)


    \frac{1+\cos{x}}{\sin{x}} + \frac{\sin{x}}{1+\cos{x}} = 2\csc{x}

    \frac{1+\cos{x}}{\sin{x}} + \frac{\sin{x}}{1+\cos{x}} \cdot \frac{1-\cos{x}}{1-\cos{x}} =

    \frac{1+\cos{x}}{\sin{x}} + \frac{\sin{x}(1-\cos{x})}{1-\cos^2{x}} =<br />

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

    \frac{1+\cos{x}}{\sin{x}} + \frac{1-\cos{x}}{\sin{x}} =

    \frac{1+\cos{x} + 1 - \cos{x}}{\sin{x}} =

    \frac{2}{\sin{x}} = 2\csc{x}
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