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Math Help - trig identitys

  1. #1
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    trig identitys

    Prove these identitys

    sinO/1+cosO=1-cosO/sinO

    1-tanO= -tanO(1-1/tanO)
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  2. #2
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    Quote Originally Posted by andrewpark2 View Post
    Prove these identitys

    sinO/1+cosO=1-cosO/sinO

    1-tanO= -tanO(1-1/tanO)
    for the first one, multiply the left side by \frac{1 - \cos{O}}{1 - \cos{O}}
    note that 1 - \cos^2{O} = \sin^2{O}


    for the second one, just distribute the right side
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  3. #3
    Member great_math's Avatar
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    Quote Originally Posted by andrewpark2 View Post
    Prove these identitys

    1-tanO= -tan O(1-1/tan O)
    <br />
1-\tan O=-\tan O\left(1- \frac 1{\tan O}\right)

    Consider RHS -\tan O\left(1- \frac 1{\tan O}\right)

    \implies \tan O\left(\frac 1{\tan O}-1\right)

    \implies \tan O\left(\frac {1-\tan O}{\tan O}\right)

    \implies 1-\tan O=LHS
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