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Math Help - trig proofs

  1. #1
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    trig proofs

    i need help solving this problem
    (seca-tana)^2=1-sina/1+sina
    any help would be appreciated
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  2. #2
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    First thing with trig proofs, you need to decide which side to work with, its best to limit your self to solving one side.
    I would start with factoring out (seca-tana)^2
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  3. #3
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    Hello, speedy229!

    (\sec\theta-\tan\theta)^2\:=\:\frac{1-\sin\theta}{1+\sin\theta}

    Multiply the right side by \frac{1-\sin\theta}{1-\sin\theta}\!:

    . . \frac{1-\sin\theta}{1+\sin\theta}\cdot{\color{blue}\frac{1-\sin\theta}{1-\sin\theta}} \;\;=\;\;\frac{(1-\sin\theta)^2}{1-\sin^2\!\theta} \;\;=\;\;\frac{(1-\sin\theta)^2}{\cos^2\!\theta}

    . . = \;\;\left(\frac{1-\sin\theta}{\cos\theta}\right)^2 \;\;=\;\;\left(\frac{1}{\cos\theta} - \frac{\sin\theta}{\cos\theta}\right)^2 \;\;=\;\;(\sec\theta - \tan\theta)^2

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  4. #4
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    trig proofs

    thanks for the help but i need to solve for 1-sina/1+sina
    i have problem solved to this point (1-sina)(1+sina/1-sin^2a this is where i'm stuck!!!!
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  5. #5
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    Quote Originally Posted by speedy229 View Post
    thanks for the help but i need to solve for 1-sina/1+sina
    i have problem solved to this point (1-sina)(1+sina/1-sin^2a this is where i'm stuck!!!!
    Your post makes no sense. Soroban has solved the problem for you!

    By the way, just in case you think it's an equation that has to be solved for a ..... It's NOT. It's an identity (as Soroban has clearly shown) and is true for all values of a.
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  6. #6
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    I think what you mean is that the answer in the back of your book has
    (1-sina)/(1+sina)= (1-sina)/(1+sina) as the proof for the identities.
    If that is the case start with the left side of the equation (seca-tana)^2 and use your identities to work towards the (1-sina)/(1+sina).
    Soroban just proved the identity by working on the right side first, I'm sure your instructor will tell you that either method is a valid solution.
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