(a)[2]
By sketching an appropriate pair of graphs, show that the equation $\sec x = 2 - \frac{1}{2}x$ has exactly one root in the interval $0 \le x < \frac{1}{2}\pi$.
(b)[2]
Verify by calculation that this root lies between $0.8$ and $1$.
(c)[3]
Use the iterative formula $x_{n+1} = \cos^{-1}\!\left(\frac{2}{4 - x_n}\right)$ to find the root correct to $2$ decimal places. Give the value from each iteration to $4$ decimal places.