(1+cos3t)/(sin3t)+(sin3t)/(1+cos3t)=2csc3t

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- anonymous

(1+cos3t)/(sin3t)+(sin3t)/(1+cos3t)=2csc3t

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- anonymous

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

- anonymous

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

- anonymous

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

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## More answers

- anonymous

ok let me look at it

- anonymous

no go, have no idea what is next

- anonymous

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

- anonymous

cotx=1/tanx

- anonymous

cscx=1/sinx

- anonymous

what else for cotx? there should be one more

- anonymous

cosx/sinx

- anonymous

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

- anonymous

sorry you lost me...

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

you are welcome

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