Target Mathematics

3.70: Cosec identity and equation

0606/23/O/N/21 — Question 5 · 8 marks

(a)
Show that cosecxsinx=cotxcosx\mathrm{cosec}\,x - \mathrm{sin}\,x = \mathrm{cot}\,x\,\mathrm{cos}\,x.
[4]
(b)
Hence solve the equation cosecxsinx=cosecxcosx\mathrm{cosec}\,x - \mathrm{sin}\,x = \mathrm{cosec}\,x\,\mathrm{cos}\,x for 0<x<3600^{\circ} < x < 360^{\circ}.
[4]