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Hannah_Ahn

  • 2 years ago

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

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

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

  3. Hannah_Ahn
    • 2 years ago
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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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  18. Mertsj
    • 2 years ago
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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.

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

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

  21. Mertsj
    • 2 years ago
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    ty

  22. Hannah_Ahn
    • 2 years ago
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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?

  23. Mertsj
    • 2 years ago
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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.

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

  25. Mertsj
    • 2 years ago
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    yw

  26. Hannah_Ahn
    • 2 years ago
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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 ?

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