Question

I need help proving one more identity: (cos(x) / (1 + cos(x))) + cos(x) / (1 - cos(x)) = 2cot(x) csc(x)
Will give medal & fan.

I have all the step-by-step, but I need the reasons. I'll post the steps in the comments.

Answer 1

I think you should use that sheet now.

Answer 2

This one is still confusing me though /: Can I tell you what I think the reason is and you tell me if it's correct or incorrect?

Answer 3

Try it once and then get your answers confirmed :)

Answer 4

Oh yeah sure :)

Answer 5

What sheet?

Answer 6

lol, really?

Answer 7

or the other one which i game her.She doesn't know the formulas .-.

Answer 8

gave*

Answer 9

Take cos x outside and the you have the eqn...
Cosx[(1/1+cosx)+(1/1-cosx)]
Solve this and you get Cosx[2/(1-cosx^2)]
Then you have Cosx[2/sinx^2]
By simplifying....you get the solution

Answer 10

First figure out how to combine the fractions together. Find the least common demominator.

Answer 11

The first step is:
(cos(x) / (1 + cos(x))) + (cos(x) / (1 - cos(x))) = ((cos(x)(1 - cos(x)) + cos(x)(1 + cos(x))) / (1 + cos(x))(1 - cos(x))

I just can't figure out what would make it all cos(x) /: I'm finding csc = 1/sin and cot = 1/tan

Answer 12

You mean, you have all the steps already but you still can't figure it out?

Answer 13

I need to put reasons with the steps...

Answer 14

Yeah I'm kind of stupid, you got me. And I'm not being sarcastic.

Answer 15

What kind of reasons are they expecting you to give for this?

Answer 16

lulz

Answer 17

I guess the basic identities they're using to get those steps? I'm not really sure

Answer 18

You have to understand I don't get a lot of instruction with this. My teacher does nothing for me except grade my work. I teach myself everything, without guidance. And this is quite difficult for me.

Answer 19

I think for the first step, since you are multiplying both fractions by the equivalent of 1 you can say

\(\dfrac{\cos(x) + 1}{\cos(x) + 1} = 1\) and \(\dfrac{1 - \cos(x) }{1 - \cos(x) } = 1\)

Answer 20

Are you sure? I mean I know you know better than I do lol but all the cos's are confusing me

Answer 21

Multiplying each of the fractions by the equivalent of one is the only way to get the LCD necessary to combine the fractions.

Answer 22

This is the problem I'm working on w/ the steps included.

Answer 23

Yep, it's exactly what I said.

Answer 24

So what would I do for the second step?

Answer 25

The second step would be to factor?

Answer 26

no. I misread

Answer 27

Ohh okay

Answer 28

simplify. cos^2 x gets cancel out
you have + and -

Answer 29

the denominator uses pythagorean

Answer 30

In the second step, cos(x) is distributed

Answer 31

since \(\cos(x)(1 + \cos(x)) = \cos(x) + \cos^2x\)

Answer 32

and \(\cos(x)(1 - \cos(x)) = \cos(x) - \cos^2x\)

Answer 33

@nincompoop, she already has the steps.

Answer 34

She needs the "reasons" for each step.

Answer 35

I am so confused... I got step 2 from you but now I'm stuck on step three lol

Answer 36

I'm surprised you can't figure out how to get to step 3 from step 2

Answer 37

What's \(\cos^2(x) - \cos^2(x)\)?

Answer 38

0

Answer 39

What's \(\cos(x) + \cos(x)\)?

Answer 40

2cos(x)

Answer 41

Okay so there you go.

Answer 42

Oh and also for the denominator

Answer 43

And I guess 1 - cos(x) is sin^2 (x)?

Answer 44

Pythagorean Identity rule applies

Answer 45

Listing reasons is almost kind of pointless here.

Answer 46

I know but if I don't do it I get a 0 on it so x_x

Answer 47

For the fourth step is sin^2 (x) divided into the numerator to become 2(cos(x) / sin(x))(1/sin(x)) ?

Answer 48

The fourth step is more of what happens when you write

\(\dfrac{4}{a^2}\) as \(\left(\dfrac{4}{a}\right)\left(\dfrac{1}{a}\right)\)

Answer 49

... I don't understand that /:

Answer 50

oh wait.. yeah I do but what would be a?

Answer 51

Oh wait I think I got it, thanks