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Diana0920 Group Title

cot(theta)-tan(theta) over sin(theta) + cos(theta) equals csc(theta) - sec(theta) how do I proof this?

  • 11 months ago
  • 11 months ago

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  1. Mertsj Group Title
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    Let's use x instead of theta

    • 11 months ago
  2. Diana0920 Group Title
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    okay

    • 11 months ago
  3. Mertsj Group Title
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    \[\frac{\cot x-\tan x}{\sin x+\cos x}=\csc x-\sec x\]

    • 11 months ago
  4. Mertsj Group Title
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    Do I have the problem stated correctly?

    • 11 months ago
  5. Diana0920 Group Title
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    yes :)

    • 11 months ago
  6. Diana0920 Group Title
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    would I have to replace cot(x) with cos(x)/sin(x)

    • 11 months ago
  7. Diana0920 Group Title
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    and tan(x) with sin(x)/cos(x)

    • 11 months ago
  8. Mertsj Group Title
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    \[(\frac{\frac{\cos x}{\sin x}-\frac{\sin x}{\cos x}}{\sin x+\cos x})\times \frac{\sin x \cos x}{\sin x \cos x}=\frac{\cos ^2x-\sin ^2x}{\sin x \cos x(\sin x+\cos x)}\]

    • 11 months ago
  9. Mertsj Group Title
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    Can you get it from there?

    • 11 months ago
  10. Diana0920 Group Title
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    sadly no? can you explain how I can simplify it more please?

    • 11 months ago
  11. Mertsj Group Title
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    Factor the numerator and then the cosx + sinx will cancel.

    • 11 months ago
  12. alejandrop95 Group Title
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    I'm still lost :(

    • 11 months ago
  13. Mertsj Group Title
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    @alejandrop95 This is not your question

    • 11 months ago
  14. Diana0920 Group Title
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    how would I factor it though? I'm sorry I am new to trig.

    • 11 months ago
  15. Mertsj Group Title
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    Can you factor this: \[a^2-b^2\]

    • 11 months ago
  16. Diana0920 Group Title
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    I don't think you can because it doesn't have the same coefficient

    • 11 months ago
  17. Mertsj Group Title
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    \[a^2−b^2=(a-b)(a+b)\]

    • 11 months ago
  18. Mertsj Group Title
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    \[\cos ^2x-\sin ^2x=(\cos x-\sin x)(\cos x+\sin x)\]

    • 11 months ago
  19. Diana0920 Group Title
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    oh okay that makes sense. so would it be cos-sin(cos+sin)

    • 11 months ago
  20. Mertsj Group Title
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    yes

    • 11 months ago
  21. Diana0920 Group Title
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    then that would cancel with the denominator correct?

    • 11 months ago
  22. Mertsj Group Title
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    Yes. sinx + cosx will cancel

    • 11 months ago
  23. Diana0920 Group Title
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    which will leave 1/sin(x)+cos(x)

    • 11 months ago
  24. Mertsj Group Title
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    no

    • 11 months ago
  25. Diana0920 Group Title
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    using the reciprocal identities this will equal csc(x)-sec(x) ?

    • 11 months ago
  26. Mertsj Group Title
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    |dw:1382579245755:dw|

    • 11 months ago
  27. Diana0920 Group Title
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    cos(x)-sin(x)/sin(x)+cos(x0

    • 11 months ago
  28. Diana0920 Group Title
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    this is where I would use the reciprocal identities?

    • 11 months ago
  29. Mertsj Group Title
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    |dw:1382579370642:dw|

    • 11 months ago
  30. Diana0920 Group Title
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    the cos(x) cancel and the sin(x) cancels?

    • 11 months ago
  31. Mertsj Group Title
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    |dw:1382579509266:dw|

    • 11 months ago
  32. Diana0920 Group Title
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    yay!!!! the cancel and its one,which now you are left with the csc(x) and sec(x) reciprocal identities!! Thank you!! the key idea here that I need to work on was the factoring

    • 11 months ago
  33. Diana0920 Group Title
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    thank you !:)

    • 11 months ago
  34. alejandrop95 Group Title
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    thanks ! :)

    • 11 months ago
  35. Mertsj Group Title
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    yw

    • 11 months ago
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