Target Mathematics

2.31: Cosecant–cotangent over 1 − cos

0606/23/O/N/19 — Question 2 · 5 marks

(i)
Show that csc⁡x−cot⁡x1−cos⁡x=csc⁡x\dfrac{\csc x - \cot x}{1 - \cos x} = \csc x.
[3]
(ii)
Hence solve csc⁡x−cot⁡x1−cos⁡x=2\dfrac{\csc x - \cot x}{1 - \cos x} = 2 for 0°<x<180°0^{\degree} < x < 180^{\degree}.
[2]