Question

Wow. Here it goes. Any ideas about how to prove this?
(1+cosx)/(1-cosx) + (1+sinx)/(1-sinx) = (2(cosx-cscx))/(cotx-cosx-cscx+1)

Answer 1

\[\frac{ 1+\cos(x) }{ 1-\cos(x) }+\frac{ 1+\sin(x) }{ 1-\sin(x) }=2\frac{ \cos(x)-\csc(x) }{ \cot(x)-\cos(x)-\csc(x)+1 }\]

Answer 2

just wanted to rewrite this first to see it better.

Answer 3

Thanks! It does look better.

Answer 4

Looks scary actually!

Answer 5

Something tells me it looks more intimidating than it is.

Answer 6

I hope you are right because my brain hurts at this point.

Answer 7

I hope you're still there and the typing is just long???

Answer 8

I think the problem may just want you to rearrange terms to prove they are equal but I'm not entirely sure.

Answer 9

Should be a problem where we manipulate the left side so it becomes matched to the right.

Answer 10

I didn't use any identities to show they are equal but I wonder if they are looking for a simpler answer using trig identities.

Answer 11

ok well then all I did was algebra to find an answer.

Answer 12

You make it sound easy. Will you share?

Answer 13

\[\frac{1-\sin(x)+\cos(x)-\sin(x)\cos(x) }{ 1-\sin(x)-\cos(x)+\sin(x)\cos(x) }+\frac{ 1-\cos(x)+\sin(x)-\sin(x)\cos(x) }{ 1-\sin(x)-\cos(x)+\sin(x)\cos(x) }=2\frac{ \cos(x)-\frac{ 1 }{ \sin(x) } }{ \frac{ \cos(x)-1 }{ \sin(x) }-\cos(x)+1 }\]

Answer 14

basically just tedious algebra, seems the post was cut off but its a lotta of distribution.

Answer 15

this is the initial setup.

Answer 16

Thanks. It is a bonus question anyway but I am desperate for every point right now. Math has always come easy for me till now. I study constantly and am still struggling.

Answer 17

No problem, this seems to mostly be a problem to keep you busy rather than stretching your understanding.

Answer 18

my final answer was \[\frac{ 2-2\sin(x)\cos(x) }{ (1-\cos(x))(1-\sin(x)) } = ""\]

Answer 19

Thanks for your help.

Answer 20

No problem and good luck.

Answer 21

I worked it through that far with your help, but can't figure out hos tomkeepmgoing to get it to equal the right side. Any more ideas?

Answer 22

Wow. My typing shows I am getting really sleepy.