Can anyone verify this identity?

Apr 2017
2
0
Philippines
cot(x) / csc^2(x) + csc(x)cot(x)-1 = sin(x)/(1+cos(x))


I tried using the fundamental identities but got stuck at some point or another. Any help is appreciated, thanks!
 
May 2016
1,310
551
USA
So we don't waste time going over what you already tried, please show us what you have already done. That makes it easy to identify where you may have made a mistake.
 

greg1313

Forum Staff
Oct 2008
8,007
1,174
London, Ontario, Canada - The Forest City
cot(x) / csc^2(x) + csc(x)cot(x)-1 = sin(x)/(1+cos(x))
I'm not sure that's correct (could be wrong, though). Are you sure that's the question?
 

skeeter

Math Team
Jul 2011
3,196
1,724
Texas
cot(x) /(csc^2(x) + csc(x)cot(x)-1) = sin(x)/(1+cos(x))


I tried using the fundamental identities but got stuck at some point or another. Any help is appreciated, thanks!
parentheses, parentheses, parentheses ...


in the denominator, note that $\csc^2{x} = 1 + \cot^2{x}$ ...
 
  • Like
Reactions: 2 people
Apr 2017
2
0
Philippines
cot(x) / csc^2x + cscxcotx-1 = sinx/1+cosx
Working on left-hand side

cot(x) / csc^2x + cscxcotx-1
cot(x) / 1+cot^2x +cscxcotx-1
**cancel out constants**

cot(x) / cot^2x+cscxcotx
cot(x) / cotx(cotx+csx)

cot(x) / cotx(cotx+csx)
**cancel out cotx**

1 / (cotx+csx) = sin(x)/(1+cos(x))

And im stuck on what to do here next.



ps: Sorry if my formatting is not so good yet. I only just joined.
 
Last edited:

skeeter

Math Team
Jul 2011
3,196
1,724
Texas
cot(x) / (csc^2x + cscxcotx-1) = sinx/(1+cosx) parentheses
Working on left-hand side

cot(x) / (csc^2x + cscxcotx-1) parentheses
cot(x) / (1+cot^2x +cscxcotx-1) parentheses
**cancel out constants**

cot(x) / (cot^2x+cscxcotx) parentheses
cot(x) / [cotx(cotx+csx)] brackets

cot(x) / [cotx(cotx+csx)] brackets

1 / (cotx+csx) = sin(x)/(1+cos(x))

And im stuck on what to do here next.
$\dfrac{1}{\cot{x}+\csc{x}} \cdot \dfrac{\sin{x}}{\sin{x}}$ ... finish it.
 
  • Like
Reactions: 1 person