Target Mathematics

2.19: Reciprocal sine identity and equation

0606/22/O/N/18 — Question 8 · 8 marks

(i)
Show that 11sinx11+sinx=2tanxsecx\dfrac{1}{1 - \sin x} - \dfrac{1}{1 + \sin x} = 2\tan x \sec x.
[4]
(ii)
Hence solve the equation 11sinx11+sinx=cscx\dfrac{1}{1 - \sin x} - \dfrac{1}{1 + \sin x} = \csc x for 0°x360°0^{\degree} \le x \le 360^{\degree}.
[4]