## Hannah_Ahn 3 years ago prove the identity: [\left( \cos2x \over \sin x \right) = \left( \cot^2x-1 \over \csc x \right)\]

1. Hannah_Ahn

$\left( \cos2x \over \sin x \right) = \left( \cot^2x-1 \over \csc x \right)$

2. Mertsj

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3. Hannah_Ahn

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

Because cos(2x) = cos^2(x)-sin^2(x)

5. Mertsj

Look at your trig double angle formulas

6. Hannah_Ahn

ohh aha! thanks. where did sin^2x come from

7. Mertsj

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8. Hannah_Ahn

yea i meant shouln't you get cos^2-sinx over sinx instead of cos^2x -sin^2x over sinx

9. Mertsj

And...|dw:1325731384713:dw|

10. Hannah_Ahn

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

11. Mertsj

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12. Hannah_Ahn

thanks! i always thought |dw:1325731485027:dw|

13. Mertsj

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14. Hannah_Ahn

hehe i learned something 8p im always so confused .. : Sdfksj skJ anyway okay keep going please

15. Mertsj

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16. Hannah_Ahn

ohhhhhhh!!!!!!!!!!!!!!! you can always work out right side instead of the left side too right? thanks!!!!!!!!!!!!!!! :P

17. Hannah_Ahn

Thanks alot for being patient with me :) and your explanation is great and quite fast! :)

18. Mertsj

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

Well I could go faster if I knew how to make fractions with the equation thing.

20. Hannah_Ahn

you just type out 'over'

21. Mertsj

ty

22. Hannah_Ahn

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

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

oh wow, i see. well thanks again :) your help is always appreciated! :)

25. Mertsj

yw

26. Hannah_Ahn

i got stuck again.. $\left( cosx \over 1+sinx \right) = \left( 1-sinx \over cosx \right)$ what should be the nxt step ?