Target Mathematics

2.3: Prove sec identity and solve modulus equation

0606/21/M/J/17 — Question 11 · 8 marks

(i)
Prove that sin⁡x(cot⁡x+tan⁡x)=sec⁡x\sin x(\cot x + \tan x) = \sec x.
[4]
(ii)
Hence solve the equation ∣sin⁡x(cot⁡x+tan⁡x)∣=2|\sin x(\cot x + \tan x)| = 2 for 0°≤x≤360°0^{\degree} \le x \le 360^{\degree}.
[4]