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anonymous

  • one year ago

helpppppppp please.

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @Hero

  3. DanJS
    • one year ago
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    What do you want to do with that?

  4. anonymous
    • one year ago
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    Simplify the trigonometric expression. Show your work.

  5. DanJS
    • one year ago
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    if you want to combine the two fractions, need to multiply by a common denominator

  6. anonymous
    • one year ago
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    okay... idk how to do that?

  7. DanJS
    • one year ago
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    \[[\frac{ 1 }{ 1+\sin \theta }+\frac{ 1 }{ 1-\sin \theta }]*\frac{ (1+\sin \theta)(1-\sin \theta) }{ (1+\sin \theta)(1-\sin \theta) }\]

  8. DanJS
    • one year ago
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    Just multiplying the whole thing by 1... a ratio of something over itself

  9. anonymous
    • one year ago
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    okay.. what does sin o stand for?

  10. anonymous
    • one year ago
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    is it kinda like pi=3.14? does it stand for a number?

  11. anonymous
    • one year ago
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    can u do it step by step and explain..

  12. jdoe0001
    • one year ago
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    one sec

  13. jdoe0001
    • one year ago
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    \(\bf \cfrac{1}{1+sin(\theta)}+\cfrac{1}{1-sin(\theta)}\impliedby LCD\to [1+sin(\theta)][1-sin(\theta)] \\ \quad \\ \cfrac{(1-sin(\theta))+(1+sin(\theta))}{[1+sin(\theta)][1-sin(\theta)]}\implies \cfrac{1\cancel{-sin(\theta)}+1\cancel{+sin(\theta)}}{[1+sin(\theta)][1-sin(\theta)]} \\ \quad \\ ----------------------------------\\ \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\qquad thus\\ ---------------------------------- \\ \quad \\ \cfrac{1\cancel{-sin(\theta)}+1\cancel{+sin(\theta)}}{{\color{brown}{ [1^2-sin^2(\theta)] }}}\implies \cfrac{2}{{\color{brown}{ cos^2(\theta)}}} \\ \quad \\ 2\cdot \cfrac{1}{cos^2(\theta)}\implies 2sec^2(\theta)\)

  14. jdoe0001
    • one year ago
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    the denominator is combined, since it's just a difference of squares and keep in mind that \(\bf sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)={\color{brown}{ 1-cos^2(\theta)}}\)

  15. jdoe0001
    • one year ago
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    woops, darn that came out off lemme redo that

  16. jdoe0001
    • one year ago
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    \(\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)={\color{brown}{ 1-sin^2(\theta)}}\) rather

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spraguer (Moderator)
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is replying to Can someone tell me what button the professor is hitting...

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