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SugarRainbow Group Title

combine the fractions and simplify to a multiple of a power of a basic trigonometric function sinx/cot^2x-sinx/cos^2x?

  • 2 years ago
  • 2 years ago

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  1. SugarRainbow Group Title
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    can i change the sinx/cos^2x into tan^2x?

    • 2 years ago
  2. zepdrix Group Title
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    Hmm no. You can take ONE of the cosines, and change it to tanx*(1/cosx) But I dont know if that's the right way to go c: hmm

    • 2 years ago
  3. zepdrix Group Title
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    \[\large \frac{ \sin x }{ \cot^2 x }-\frac{ \sin x }{ \cos^2 x }=\frac{ \sin x }{ (\frac{ \cos^2 x }{ \sin^2 x }) }-\frac{ \sin x }{ \cos^2 x }\] \[\large \frac{ \sin x }{ 1 }*\frac{ \sin^2 x }{ \cos^2 x }-\frac{ \sin x }{ \cos^2 x }\]

    • 2 years ago
  4. zepdrix Group Title
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    There are multiple ways to simplify it, since there are so many trig identities, so you might find a different way... but this is what I was thinking :3

    • 2 years ago
  5. zepdrix Group Title
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    \[\large \frac{ \sin^3 x - \sin x }{ \cos^2 x }\]

    • 2 years ago
  6. zepdrix Group Title
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    Confused about any of that so far? :D

    • 2 years ago
  7. SugarRainbow Group Title
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    how did you get sinx/1∗sin^2x/cos^2x

    • 2 years ago
  8. zepdrix Group Title
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    \[\large \frac{ \left(\frac{ a }{ b }\right) }{ \left(\frac{ c }{ d }\right) }=\frac{ a }{ b }*\frac{ d }{ c }\]

    • 2 years ago
  9. zepdrix Group Title
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    Remember how you can do that? when dividing fractions :D flip the bottom one and rewrite it as multiplication.

    • 2 years ago
  10. SugarRainbow Group Title
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    but the top wasn't a fraction yet it was sinx/ (cos^2x/sin^2x)

    • 2 years ago
  11. SugarRainbow Group Title
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    oh wait you put it over 1 to make it into a fraction huh?

    • 2 years ago
  12. zepdrix Group Title
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    \[\huge \frac{ \left(\sin x \right) }{ \left(\frac{ \cos^2 x }{ \sin^2 x } \right) }=\frac{ \left(\frac{ \sin x }{ 1 } \right) }{ \left(\frac{ \cos^2 x }{ \sin^2 x } \right) }\]

    • 2 years ago
  13. zepdrix Group Title
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    Yah hehe :3

    • 2 years ago
  14. zepdrix Group Title
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    I gotta go, so lemme post the rest of the steps, and you can at least look at them while I'm gone. I won't be here to answer questions though :c

    • 2 years ago
  15. SugarRainbow Group Title
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    okay

    • 2 years ago
  16. zepdrix Group Title
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    \[\large \frac{ \sin^3 x - \sin x }{ \cos^2 x }=\frac{ \sin x(\sin^2 x - 1) }{ 1-\sin^2 x }\]

    • 2 years ago
  17. zepdrix Group Title
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    Factored a sinx from each term in the top. Rewrote cos^2 as 1-sin^2 using identity :D

    • 2 years ago
  18. zepdrix Group Title
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    Now if we factor a -1 ouch of each term in the top brackets, we'll have a nice easy cancellation.

    • 2 years ago
  19. zepdrix Group Title
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    \[\large \frac{ -\sin x(1-\sin^2 x) }{ 1-\sin^2 x }=-\sin x\]

    • 2 years ago
  20. zepdrix Group Title
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    Hopefully I didn't make a mistake in there :D heh

    • 2 years ago
  21. SugarRainbow Group Title
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    alright well thanks

    • 2 years ago
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