Question

How would you go about proving the identity of:
(1/1)-[sin^2 theta/(1+cos theta)]=2 csc theta

Answer 1

\[\Large \frac{1}{1}-\frac{\sin^2 \theta}{1+\cos \theta}=2 \csc \theta\]

Answer 2

Is this your equation?

Answer 3

\(\LARGE\color{blue}{ \ \frac{1}{1} -\frac{\sin^2θ}{1+\cosθ} =2\cscθ }\)

\(\LARGE\color{blue}{ \ \frac{1+\cosθ}{1+\cosθ} -\frac{\sin^2θ}{1+\cosθ} =2\cscθ }\)

\(\LARGE\color{blue}{ \ \frac{1+\cosθ-\sin^2θ}{1+\cosθ} =2\cscθ }\)

Answer 4

I got disconnected in the middle of typing -:(

Answer 5

Yes, it is my equation.

Answer 6

You're fine! I truly appreciate the help!

Answer 7

\(\large\color{blue}{ \ 1+\cosθ-\sin^2θ =2\cscθ(1 +\cosθ)}\)

I don't know how to finish, sorry.

Answer 8

It's fine, you've helped me so much already! I can solve it from here :)

Answer 9

It's not identity, how to prove. This is counterexample
x = pi/2 --> sin x = 1, sin^2 =1 and csc (x) =1 also
The left hand side is \(1-\dfrac{sin^2x}{(1+cosx)}= 1-\dfrac{1}{1}=0\)
while the right hand side 2csc (x) =2
If it is identity, then 0 =2????

Answer 10

One more question: solve or prove??

Answer 11

It's listed under identities. That I was asked to verify. I'm sorry.

Answer 12

It says to verify/establish

Answer 13

No need to say sorry, it's not your fault. Can you post the page? ( please, scan and attach)

Answer 14

okay, please give me a moment.

Answer 15

One more thing: hehehe.. I am annoyed, right? verify or justify??

Answer 16

Verify.

Answer 17

hihihi... I fail with you. You are not alone.

Answer 18

It's problem number four.

Answer 19

Thank you again.

Answer 20

hey, your number four has the right hand side is cos, not csc

Answer 21

you intermingle number3 and number 4
left hand side: number4
right hand side number 3
ha!!

Answer 22

so, you fail alone, me not. hihihihi

Answer 23

Did I really?

Answer 24

check it by yourself.

Answer 25

I did!! I am so sorry!

Answer 26

Ye, should say sorry to @SolomonZelman It's your fault.

Answer 27

why are you saying sorry to me ? @Loser66

Answer 28

I am so sorry @SolomonZelman for mistyping my problem.

Answer 29

me not, the asker should say sorry to you only. It's her fault, not mine. hehehe...

Answer 30

okay... ;)