Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

ok let me look at it

Answer 5

no go, have no idea what is next

Answer 6

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

Answer 7

cotx=1/tanx

Answer 8

cscx=1/sinx

Answer 9

what else for cotx? there should be one more

Answer 10

cosx/sinx

Answer 11

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

Answer 12

sorry you lost me...

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

you are welcome