## skybunnygirl Group Title (1+cos3t)/(sin3t)+(sin3t)/(1+cos3t)=2csc3t one year ago one year ago

1. Hoa Group Title

$\frac{ 1+\cos3t }{ \sin3t }+\frac{ \sin3t }{ 1+\cos3t }= 2\csc3t$ what do you want? prove it?

2. skybunnygirl Group Title

yes please, im having the hardest time with these questions...

3. Hoa Group Title

I give you idea, you do the rest. the first part $\frac{ 1+\cos3t }{ \sin3t }= \frac{ 1 }{ \sin3t }+ \frac{ \cos3t }{ \sin3t }= \csc 3t + \cot 3t$

4. skybunnygirl Group Title

ok let me look at it

5. skybunnygirl Group Title

no go, have no idea what is next

6. Zebo Group Title

That is pretty much it. You know what cot(x) is equal to? Also what is csc(x) equal to.

7. skybunnygirl Group Title

cotx=1/tanx

8. skybunnygirl Group Title

cscx=1/sinx

9. Zebo Group Title

what else for cotx? there should be one more

10. skybunnygirl Group Title

cosx/sinx

11. Zebo Group Title

now look at the first step, do you see something similar to what you said

12. skybunnygirl Group Title

sorry you lost me...

13. Zebo Group Title

you said cotx = cosx/sinx and you said cscx=1/sinx right?

14. skybunnygirl Group Title

yes and that is what we converted into part of the original problem

15. Hoa Group Title

ok I give you mine : from yours , right side = 2/ sin3t. write it out

16. Hoa Group Title

now I just prove that left side * sin 2t =2, right? it is easy to do

17. Hoa Group Title

$\sin 3t \left[ \frac{ 1 + cost 3t }{ \sin3t } +\frac{ \sin3t }{ 1 + \cos 3t } \right]$

18. Hoa Group Title

$= \frac{ \sin 3t + \cos 3t }{ \sin3t }+ \frac{ \sin^2 3t }{ 1 + \cos 3t }$

19. skybunnygirl Group Title

ok, how did we get from csc3t+cot3t+sin3t/1+cos3t to what you writing now?

20. Hoa Group Title

$= (\frac{ sint }{ \sin3t }+ \frac{ \sin3tcos3t }{ \sin3t }+ \frac{ 1-\cos^2 3t }{1+\cos 3t })$

21. Hoa Group Title

$=1+ \cos 3t + \frac{ (1+\cos3t)(1-\cos3t) }{ 1+\cos 3t }$

22. Hoa Group Title

and then you have 1+1 =2. the proof done. is it clear?

23. Hoa Group Title

I make the right side2 csc 3t = 2/ sin3t. and then time both sides to sin 3t

24. Hoa Group Title

do you get mine? think of it. write out and it will make sense to you.

25. skybunnygirl Group Title

ok let me look at it and see, im still not sure why we did the very first step as we ended up working out the original set up

26. Hoa Group Title

our goal is prove the original equation is true, that means you must prove the left side = right side. some equation is not true at all, for example : how can you prove 1+1 =3? fortunately, your problem is prove it true, that means it is true already, just explain in which logic, it is true. done

27. skybunnygirl Group Title

ok, let me work it out on paper and see what I come up with. Thanks for your help.

28. Hoa Group Title

you are welcome