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anonymous

  • one year ago

sec-tan=cos/1+sin I have to get the left to become the right without changing the right hand side using trig fomulas

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  1. anonymous
    • one year ago
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    So how can you rewrite the left-hand side to start out?

  2. anonymous
    • one year ago
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    yes

  3. anonymous
    • one year ago
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    No, how would you do it? Just making sure you know how to start, lol.

  4. anonymous
    • one year ago
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    I changed the sec and tan to 1/cos and sin/cos

  5. anonymous
    • one year ago
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    Right. And both of those fractions have a denominator of cos and can thus be combined into \(\frac{1-sinx}{cosx}\) I'm sure that makes sense. From there, the trick is to multiply top and bottom by the conjugate of the numerator. As in multiply top and bottom by 1+sinx. So what would the numerator become if you wee to do that?

  6. anonymous
    • one year ago
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    (1-sin^2)/cos(1+sin)?

  7. anonymous
    • one year ago
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    Exactly. And you can use an identity on the \(1-sin^{2}x\)

  8. anonymous
    • one year ago
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    cos^2/(1+sin)

  9. anonymous
    • one year ago
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    RIght, you would now have \[\frac{ \cos^{2}x }{ cosx(1+sinx) }\] which from there you can seen how one of the cosines would cancel and youd have the result youre looking for :)

  10. anonymous
    • one year ago
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    thank you so much

  11. anonymous
    • one year ago
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    No problem :)

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