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Math Help - calc fundamental identities

  1. #1
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    calc fundamental identities

    how to simplify

    sin X / 1+ cos X + 1+cos X / sin X
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  2. #2
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    Quote Originally Posted by sandman69 View Post
    how do you simplify

    sin x / 1+cos x + 1+cos x / sin x
    Hi sandman69,

    You need a common denominator

    \frac{sinx}{1+cosx}+\frac{1+cosx}{sinx}=\frac{sinx  }{sinx}\ \left(\frac{sinx}{1+cosx}\right)+\frac{1+cosx}{1+c  osx}\ \left(\frac{1+cosx}{sinx}\right)

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

    sin^2x+cos^2x=1

    so we get

    \frac{2+2cosx}{sinx(1+cosx)}=\frac{2(1+cosx)}{sinx  (1+cosx)}

    \frac{1+cosx}{1+cosx}=1

    \frac{2}{sinx}=2cosecx
    Last edited by mr fantastic; April 10th 2010 at 03:13 PM. Reason: Moved from thread caused by duplicate post
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  3. #3
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    Quote Originally Posted by sandman69 View Post
    how to simplify

    sin X /(1+ cos X) + (1+cos X)/sin X
    as shown above, please use parentheses to make your trig expression clear ...


    \frac{\sin{x}}{1+\cos{x}} + \frac{1+\cos{x}}{\sin{x}}<br />

    common denominator is \sin{x}(1+\cos{x}) ...

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

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

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

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

    \frac{2}{\sin{x}} = 2\csc{x}
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  4. #4
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    fundamental identities

    how do you do
    (tan x + cot) / (sec * csc)
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  5. #5
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    Quote Originally Posted by sandman69 View Post
    how do you do
    (tan x + cot) / (sec * csc)
    First things first remove that denominator and convert to \sin(x) and \cos(x)

    \left(\frac{\sin(x)}{\cos(x)} + \frac{\cos(x)}{\sin(x)}\right) \cdot \sin(x)\cos(x)

    For that left term get the same denominator

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

    which gives us \left(\frac{\sin^2(x)+\cos^2(x)}{\cos(x) \sin(x)}\right) \cdot \sin(x)\cos(x) = \sin^2(x) + \cos^2(x)


    You can still cancel that further using a well known identity which you must know .
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  6. #6
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    fundamental identites

    do you know wer i could find alll the rules for these.
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