(a)[2]
Sketch a suitable pair of graphs to show that the equation $\cosec x = 1 + e^{-\frac{1}{2}x}$ has exactly two roots for $0 < x < \pi$.
(b)[3]
The sequence formed by the iterative formula $x_{n+1} = \pi - \sin^{-1}\left(\frac{1}{e^{-\frac{1}{2}x_n} + 1}\right)$, with initial value $x_1 = 2$, converges to one of these roots. Use the formula to determine this root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.