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SugarRainbow

HELP SIMPLIFY (sinx/1-cosx)+(1-cosx/sinx)

  • one year ago
  • one year ago

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  1. Shadowys
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    I believe you have attempted to do it. Where were you stuck? Though the answer isn't that pretty..

    • one year ago
  2. SugarRainbow
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    okay so i was thinking of multiplying cosx to the numerator and denominator of the (sinx/1-cosx) so then the denominator will be sin^2x and then multiply sinx to (1-cosx/sinx) so that both denominators will bbe sin^2x is that even a good first step to take?

    • one year ago
  3. seitys
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    sinx/(1-cosx)*(1+cosx)/(1+cosx) + (1-cosx/sinx) =sinx(1+cosx)/sin^2 x + (1-cosx/sinx) =(1+cosx/sinx)+(1-cosx/sinx) =(1+cosx+1-cosx)/sinx =2/sinx

    • one year ago
  4. SugarRainbow
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    why did you do this sinx(1+cosx)/sin^2 x or how'd that happen

    • one year ago
  5. SugarRainbow
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    oh wait nevermind i see what you did there

    • one year ago
  6. seitys
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    when you multiply (1-cosx) by its conjugate (1+cosx), you get (1-cos^2 x) which is just sin^2 x --> sin^2 x + cos^2 x = 1 so 1-cos^2 x=sin^2 x

    • one year ago
  7. SugarRainbow
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    okay well how did that turn into (1+cosx/sinx)?

    • one year ago
  8. seitys
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    there is a sinx in the numerator and a sin^2 x in the denominator. so 1 of them cancels out.

    • one year ago
  9. SugarRainbow
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    and you got 2/sinx because the +cosx and the -cosx cancel out right?

    • one year ago
  10. seitys
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    because that is the remaining denominator for both terms.

    • one year ago
  11. seitys
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    yes

    • one year ago
  12. seitys
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    you can simplify it even further because 1/sinx = cscx so it can also be written as 2cscx

    • one year ago
  13. SugarRainbow
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    oh okay thank you this was really helpful

    • one year ago
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