Prove that (2cosec-1)/(tanx-2secx)=-cotx will give ten points for answers with workings. please help

(2cscx - 1)/(tanx - 2secx)
(2/sinx - 1) / (sinx/cosx - 2/cosx)
[(2 - sinx) / sin x] / [(sin x - 2) / cos x)]
[(2 - sin x) / sin x] * [(cos x) / (sin x - 2)]
-1 * cosx / sin x
-cosx/sinx
-cotx

Do I win?

2cosec-1 Equals 1/2cosec = 1/(2(1/sinx) = 1/(2/sinx) = (2/sinx)-1

tanx-2secx = tanx - 2(1/cosx) = tanx - (2/cosx)

tanx = sinx/cosx

so

tanx - (2/cosx) = sinx/cosx - (2/cosx)

Then you got

(2/sinx)-1 / sinx/cosx - (2/cosx) = - cosx/sinx


Cross multiply

(2/sinx)-1 * 1 = (sinx/cosx - 2/cosx) * - cosx/sinx

(2/sinx)-1 = (cosxsinx/sinxcosx - 2cosxsinx/cosx)
(2/sinx)-1 = (1 - 2sinx) = (2/sinx)-1

I don't really know how to explain.. I'm sorry.