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 April 25th, 2017, 07:40 AM #1 Newbie   Joined: Apr 2017 From: Philippines Posts: 2 Thanks: 0 Can anyone verify this identity? 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!
 April 25th, 2017, 07:53 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 924 Thanks: 369 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.
April 25th, 2017, 08:02 AM   #3
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Quote:
 Originally Posted by trisource 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?

April 25th, 2017, 08:07 AM   #4
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Quote:
 Originally Posted by trisource 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 $\csc^2{x} = 1 + \cot^2{x}$ ...

 April 25th, 2017, 10:12 AM #5 Newbie   Joined: Apr 2017 From: Philippines Posts: 2 Thanks: 0 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 by trisource; April 25th, 2017 at 10:16 AM.
April 25th, 2017, 10:40 AM   #6
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Quote:
 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.

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