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$$\frac{\csc(x)-1}{\cot(x)}=\frac{\cot(x)}{\csc(x)+1}$$ Once again, "Professor Google" provides an example that's different enough that I can't solve "my" problem. I'm beginning to think that Google does this me on purpose.

Jam
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Jim Irwin
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    Try turning everything on one side of the equation into sines and cosines, and then simplify it until you can't go any further. Then do the same with the other side and try to reach a common point. – layman Jul 27 '14 at 01:50
  • Use Wolfram Alpha alongside Google if you want a website to refer to. – Jam Jul 27 '14 at 01:52

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Hint: Pretend that this wasn't an identity problem. Does the equation look reasonable? My first instinct would be to cross-multiply. This would give me: $$ \csc^2 x - 1 = \cot^2 x $$ which is indeed a rearranged and modified version of the standard Pythagorean Identity.

So how can we go from the LHS to the RHS? Well the above work suggests that we try multiplying by the conjugate. That is, start by multiplying the LHS by: $$ \frac{\csc x + 1}{\csc x + 1} $$

Adriano
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