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Thread: Need help proving trigonometric identities?

  1. December 8th 2011, 05:42 PM #1
    ccfoose
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    Need help proving trigonometric identities?

    Could you please help me with proving these problems, i just dont get these ones
    1.) cot^2x=(cscx-1)(cscx+1)

    2.) tan^2x=sec^2x-sin^2x-cos^2x

    3.) csc^3xtan^2x=cscx(1+tan^2x)

    4.) sinx/1-cosx + sinx/1+cosx = 2cscx

    5.) sinx/cscx-1 + sinx/cscx+1 = 2tan^2x


    Please help, all is appreciated.
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  2. December 8th 2011, 05:45 PM #2
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    Re: Need help proving trigonometric identities?

    Quote Originally Posted by ccfoose View Post
    Could you please help me with proving these problems, i just dont get these ones
    1.) cot^2x=(cscx-1)(cscx+1)

    2.) tan^2x=sec^2x-sin^2x-cos^2x

    3.) csc^3xtan^2x=cscx(1+tan^2x)

    4.) sinx/1-cosx + sinx/1+cosx = 2cscx

    5.) sinx/cscx-1 + sinx/cscx+1 = 2tan^2x


    Please help, all is appreciated.
    1.
    \displaystyle \begin{align*} \left(\csc{x} - 1\right)\left(\csc{x} + 1\right) &\equiv \csc^2{x} - 1 \\ &\equiv \cot^2{x} \end{align*}


    2.
    \displaystyle \begin{align*} csc{x}\left(1 + \tan^2{x}\right) &\equiv \csc{x}\sec^2{x} \\ &\equiv \frac{1}{\sin{x}}\cdot \frac{1}{\cos^2{x}} \\ &\equiv \frac{1}{\sin{x}\cos^2{x}} \\ &\equiv \frac{\sin^2{x}}{\sin^3{x}\cos^2{x}} \\ &\equiv \frac{1}{\sin^3{x}} \cdot \frac{\sin^2{x}}{\cos^2{x}} \\ &\equiv \csc^3{x}\tan^2{x} \end{align*}


    Trigonometric identities just take a bit of playing around. I'll leave you to try the rest.
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  3. December 8th 2011, 05:48 PM #3
    ccfoose
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    Re: Need help proving trigonometric identities?

    i know how to do most of them, i just didnt understand these beacuse some some seemed too simple and or too complex. like 4 and 5, i dont understand at all!
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  4. December 8th 2011, 05:53 PM #4
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    Re: Need help proving trigonometric identities?

    Quote Originally Posted by ccfoose View Post
    i know how to do most of them, i just didnt understand these beacuse some some seemed too simple and or too complex. like 4 and 5, i dont understand at all!
    Since you haven't used brackets, I'm not exactly sure what your equations are, but I would suggest with 4 and 5 to start by getting a common denominator on the LHS.
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  5. December 8th 2011, 05:56 PM #5
    ccfoose
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    Re: Need help proving trigonometric identities?

    its like the first part is one fraction, then plus the second fraction... i always mix up my common denominators, so i was just wondering how exactly to do probems like those.
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  6. December 8th 2011, 06:02 PM #6
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    Re: Need help proving trigonometric identities?

    Quote Originally Posted by ccfoose View Post
    its like the first part is one fraction, then plus the second fraction... i always mix up my common denominators, so i was just wondering how exactly to do probems like those.
    Getting a common denominator is simple.

    \displaystyle \begin{align*} \frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{bc}{bd} = \frac{ad + bc}{bd} \end{align*}

    You won't learn anything until you try some things for yourself.
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  7. December 8th 2011, 06:10 PM #7
    ccfoose
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    Re: Need help proving trigonometric identities?

    can you do one of the ones using fractions so i can know the whole process, then i can try the other
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  8. December 9th 2011, 02:56 PM #8
    mr fantastic
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    Re: Need help proving trigonometric identities?

    Quote Originally Posted by ccfoose View Post
    can you do one of the ones using fractions so i can know the whole process, then i can try the other
    Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. See rule #8: http://www.mathhelpforum.com/math-he...hp?do=vsarules.

    Post one of these questions that you think getting help on will be of benefit in doing the others. Also, please show some effort - show all your work and say where you get stuck.

    Thread closed.
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