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Thread: Pythagorean Identities

  1. #1
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    Pythagorean Identities

    Prove that $\displaystyle secx + cosecxcotx \equiv secx cosec^2x $

    I am having real trouble with these pythagorean identities, I have the rules but don't even know where to start.
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  2. #2
    Super Member craig's Avatar
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    Quote Originally Posted by greghunter View Post
    Prove that $\displaystyle secx + cosecxcotx \equiv secx cosec^2x $

    I am having real trouble with these pythagorean identities, I have the rules but don't even know where to start.
    If you know the identities you will remember that $\displaystyle \cot^2{x} +1 = cosec^2{x}$.

    If we put this into the right hand side we get $\displaystyle secx(\cot^2{x} +1)$.

    $\displaystyle \frac{1}{\cos{x}}(\cot^2{x} +1)$

    $\displaystyle \frac{\cos^2{x}}{\sin^2{x}\cos{x}} + \frac{1}{\cos{x}}$

    Can you finish this off?
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  3. #3
    Super Member craig's Avatar
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    Oh just to note, it's perfectly legitimate to start on either side of the equation and make that equal to another.
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  4. #4
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    Thanks Craig,
    I think I just need to do some more practice on these
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  5. #5
    Super Member craig's Avatar
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    Quote Originally Posted by greghunter View Post
    Thanks Craig,
    I think I just need to do some more practice on these
    No problem. As long as you remember $\displaystyle \sin^2{x} + \cos^2{x} = 1$ this is all you need, just divide through by either $\displaystyle \sin^2{x}$ or $\displaystyle \cos^2{x}$ to get the other two.

    That's also providing you remember all the double angle formulas etc.
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