(a(i))[2]
Differentiate $\frac{1}{\cos x}$ to show that, when $y = \sec x$, $\frac{dy}{dx} = \sec x \tan x$.
(a(ii))[1]
Show that $\frac{1}{\sec x - \tan x}$ can be rewritten as $\sec x + \tan x$.
(a(iii))[2]
Deduce that $\frac{1}{(\sec x - \tan x)^2}$ equals $2\sec^2 x - 1 + 2\sec x \tan x$.
(a(iv))[3]
Hence demonstrate that $\int_0^{\frac{1}{4}\pi} \frac{1}{(\sec x - \tan x)^2} \, dx = \frac{1}{4}(8\sqrt{2} - \pi)$.