Question

Verify:
1/tanx - sinx/(cosx-1) = -cscx

I've finished most of my homework but this problem is getting on my nerves! I just need to know how to solve it, not just the answer. It's probably easy, but my brain is fried...

Answer 1

hint:
\[\frac{1}{{\tan x}} - \frac{{\sin x}}{{\cos x - 1}} = \frac{{\cos x}}{{\sin x}} - \frac{{\sin x}}{{\cos x - 1}}\]

Answer 2

Well I got that part down, but I kept thinking it was wrong because for some reason I can't get passed that point.

Answer 3

we have to compute the least common multiple between sinx and cosx-1, which is:
sinx(cosx-1)

Answer 4

\[\frac{{\cos x}}{{\sin x}} - \frac{{\sin x}}{{\cos x - 1}} = \frac{{\cos x\left( {\cos x - 1} \right) - \sin x\sin x}}{{\sin x\left( {\cos x - 1} \right)}} = ...?\]