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Hannah_Ahn

prove the identity: [\left( \cos2x \over \sin x \right) = \left( \cot^2x-1 \over \csc x \right)\]

  • 2 years ago
  • 2 years ago

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  1. Hannah_Ahn
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    \[\left( \cos2x \over \sin x \right) = \left( \cot^2x-1 \over \csc x \right)\]

    • 2 years ago
  2. Mertsj
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    |dw:1325730453048:dw|

    • 2 years ago
  3. Hannah_Ahn
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    i got it until (cos^2 over sinx) - (sinx) after your second step i multiplied deno and numerator by sinx. but how did you get cos^2-sin^2x over sinx and how is it same as cos^2x over sinx?

    • 2 years ago
  4. Mertsj
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    Because cos(2x) = cos^2(x)-sin^2(x)

    • 2 years ago
  5. Mertsj
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    Look at your trig double angle formulas

    • 2 years ago
  6. Hannah_Ahn
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    ohh aha! thanks. where did sin^2x come from

    • 2 years ago
  7. Mertsj
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    |dw:1325731291201:dw|

    • 2 years ago
  8. Hannah_Ahn
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    yea i meant shouln't you get cos^2-sinx over sinx instead of cos^2x -sin^2x over sinx

    • 2 years ago
  9. Mertsj
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    And...|dw:1325731384713:dw|

    • 2 years ago
  10. Hannah_Ahn
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    i am so sorry.. shouldn't you be dividing them by sinx not sin^2x? hahah :P

    • 2 years ago
  11. Mertsj
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    |dw:1325731527945:dw|

    • 2 years ago
  12. Hannah_Ahn
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    thanks! i always thought |dw:1325731485027:dw|

    • 2 years ago
  13. Mertsj
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    |dw:1325731638760:dw|

    • 2 years ago
  14. Hannah_Ahn
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    hehe i learned something 8p im always so confused .. : Sdfksj skJ anyway okay keep going please

    • 2 years ago
  15. Mertsj
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    |dw:1325731751062:dw|

    • 2 years ago
  16. Hannah_Ahn
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    ohhhhhhh!!!!!!!!!!!!!!! you can always work out right side instead of the left side too right? thanks!!!!!!!!!!!!!!! :P

    • 2 years ago
  17. Hannah_Ahn
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    Thanks alot for being patient with me :) and your explanation is great and quite fast! :)

    • 2 years ago
  18. Mertsj
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    You can work on either side when proving an identity or both sides. You just can't work across the equal sign like adding the same thing to both sides or something like that.

    • 2 years ago
  19. Mertsj
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    Well I could go faster if I knew how to make fractions with the equation thing.

    • 2 years ago
  20. Hannah_Ahn
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    you just type out 'over'

    • 2 years ago
  21. Mertsj
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    ty

    • 2 years ago
  22. Hannah_Ahn
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    uw. p.s. are you a tutor? like to help students? anywho when you see identity questions how do you know what to do and which side to solve first?

    • 2 years ago
  23. Mertsj
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    I used to teach math in high school for 32 years and now I am retired and tutor students who come to my house. I can usually solve identities.

    • 2 years ago
  24. Hannah_Ahn
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    oh wow, i see. well thanks again :) your help is always appreciated! :)

    • 2 years ago
  25. Mertsj
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    yw

    • 2 years ago
  26. Hannah_Ahn
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    i got stuck again.. \[\left( cosx \over 1+sinx \right) = \left( 1-sinx \over cosx \right)\] what should be the nxt step ?

    • 2 years ago
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