Target Mathematics

2.20: Tan–sec sum identity and sine equation

0606/22/O/N/19 — Question 6 · 9 marks

(i)
Show that tan⁡x1+sec⁡x+1+sec⁡xtan⁡x=2sin⁡x\dfrac{\tan x}{1 + \sec x} + \dfrac{1 + \sec x}{\tan x} = \dfrac{2}{\sin x}.
[5]
(ii)
Hence solve the equation tan⁡x1+sec⁡x+1+sec⁡xtan⁡x=1+3sin⁡x\dfrac{\tan x}{1 + \sec x} + \dfrac{1 + \sec x}{\tan x} = 1 + 3\sin x for 0°≤x≤180°0^{\degree} \le x \le 180^{\degree}.
[4]