Question 10 - A-Level Maths

Prove the identity \(\frac { 1 + \sin x } { 1 - \sin x } - \frac { 1 - \sin x } { 1 + \sin x } \equiv \frac { 4 \tan x } { \cos x }\).
Hence solve the equation \(\frac { 1 + \sin x } { 1 - \sin x } - \frac { 1 - \sin x } { 1 + \sin x } = 8 \tan x\) for \(0 \leqslant x \leqslant \frac { 1 } { 2 } \pi\).