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Math Help - Trig question pre calc!

  1. #1
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    Trig question pre calc!

    Hi there, the question states

    Prove algebraically: \cos\theta/1-sin\theta = sec\theta +(sec\theta)(csc\theta)-cot\theta

    Here are the steps i took to solving this i worked on the right side making it equal the left

    1) change all sec/ csc/ cot to their respective forms ( \1/sin\theta) and so forth

    and when i get to this point I'm lost \frac{sin\theta +1 - cos\theta^2} {cos\theta sin\theta}

    After this point I'm lost please help, i apologize if i have asked too many questions but i am trying to study for my final.

    Thanks!
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  2. #2
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    Re: Trig question pre calc!

    Hey Gurp925.

    Is it meant to be cos(theta) / [1 - sin(theta)] or cos(theta) - sin(theta)?
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  3. #3
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    Re: Trig question pre calc!

    \frac{sin\theta+1-cos^2\theta}{cos\theta sin\theta}

    =\frac{sin\theta+sin^2\theta}{cos\theta sin\theta}

    =\frac{sin\theta(1+sin\theta)}{cos\theta sin\theta}

    =\frac{1+sin\theta}{cos\theta}

    =\frac{(1+sin\theta)(1-sin\theta)}{cos\theta(1-sin\theta)}

    =\frac{1-sin^2\theta}{cos\theta(1-sin\theta)}

    =\frac{cos^2\theta}{cos\theta(1-sin\theta)}

    ...

    Hope this helps
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  4. #4
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    Re: Trig question pre calc!

    Hey Acc100jt almost understood the question just wondering how did you multiply the denominator by (1-sin) ?thus multiplying the top? if i understand that then the question is solved. Thanks everyone for their help.
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  5. #5
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    Re: Trig question pre calc!

    Quote Originally Posted by Gurp925 View Post
    Hey Acc100jt almost understood the question just wondering how did you multiply the denominator by (1-sin) ?thus multiplying the top? if i understand that then the question is solved. Thanks everyone for their help.
    Multiplying top and bottom by the bottom's conjugate.
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