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  1. #1
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    Unhappy Help proving

    I am having problems sproving a couple of equations. Thank you in advance
    1.)
    <br />
\tan{x}+cot{x}= \frac{csc^2}{cot{x}}<br />
    2.) 1-cosx
    sinx
    = sinx
    1+cosx
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  2. #2
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    Quote Originally Posted by nightrider456 View Post
    I am having problems sproving a couple of equations. Thank you in advance
    1.)
    <br />
\tan{x}+cot{x}= \frac{csc^2}{cot{x}}<br />
    2.) 1-cosx
    sinx
    = sinx
    1+cosx
    2. \frac{1 - \cos{x}}{\sin{x}} = \frac{1 - \cos{x}}{\sin{x}}\cdot\frac{1 + \cos{x}}{1 + \cos{x}}

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

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

     = \frac{\sin{x}}{1 + \cos{x}}.
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  3. #3
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    Quote Originally Posted by nightrider456 View Post
    I am having problems sproving a couple of equations. Thank you in advance
    1.)
    <br />
\tan{x}+cot{x}= \frac{csc^2}{cot{x}}<br />
    2.) 1-cosx
    sinx
    = sinx
    1+cosx
    1) Recall that \sin^2{x} + \cos^2{x} = 1.

    Dividing both sides by \sin^2{x} gives

    1 + \cot^2{x} = \csc^2{x}.


    So \frac{\csc^2{x}}{\cot{x}} = \frac{1 + \cot^2{x}}{\cot{x}}

     = \frac{1}{\cot{x}} + \cot{x}

     = \tan{x} + \cot{x}.
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