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Math Help - Prove 2 sec X = ... (Please help!)

  1. #1
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    Verify (1+sinx)/cosx + cosx/(1+sinx) = 2secx (Please help!)

    Verify:

    (1+sinx)/cosx + cosx/(1+sinx) = 2secx

    Thanks.
    Last edited by SMA777; December 8th 2008 at 02:37 PM.
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  2. #2
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by SMA777 View Post
    Verify:

    (1+sinx)/cosx + cosx/(1+sinx) = 2secx

    Thanks.
    \frac{1 + \sin{x}}{\cos{x}} + \frac{\cos{x}}{1+\sin{x}}

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

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

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

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

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

    \frac{2}{\cos{x}}

    2\sec{x}
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  3. #3
    FrY
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    \frac{1+\sin \left( x \right)}{\cos \left( x \right)}+\frac{\cos \left( x \right)}{1+\sin \left( x \right)}=2\sec \left( x \right)


    \frac{1+2\sin \left( x \right)+\sin ^{2}\left( x \right)+\cos ^{2}\left( x \right)}{\cos \left( x \right)\cdot 1+\sin \left( x \right)}=2\sec \left( x \right)<br />


    \frac{2+2\sin \left( x \right)}{\cos \left( x \right)\cdot 1+\sin \left( x \right)}=2\sec \left( x \right)


    \frac{2\cdot \left( 1+\sin \left( x \right) \right)}{\cos \left( x \right)\cdot 1+\sin \left( x \right)}=2\sec \left( x \right)


    \frac{2}{\cos \left( x \right)}=2\sec \left( x \right)

    <br />
2\cdot \frac{1}{\cos \left( x \right)}=2\sec \left( x \right)

    <br />
2\sec \left( x \right)=2\sec \left( x \right)

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  4. #4
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    Quote Originally Posted by FrY View Post
    \frac{2+2\sin \left( x \right)}{\cos \left( x \right)\cdot 1+\sin \left( x \right)}=2\sec \left( x \right)


    \frac{2\cdot \left( 1+\sin \left( x \right) \right)}{\cos \left( x \right)\cdot 1+\sin \left( x \right)}=2\sec \left( x \right)

    Could someone please explain going from {2+2\sin(x)} to {2\cdot \left( 1+\sin \left( x \right) \right)} ?
    I am unsure of how this happened.
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  5. #5
    FrY
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    Quote Originally Posted by tiar View Post
    Could someone please explain going from {2+2\sin(x)} to {2\cdot \left( 1+\sin \left( x \right) \right)} ?
    I am unsure of how this happened.
    What we did is factorize the expression 2+2\sin \left( x \right) being 2 the common factor.
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