By sketching suitable graphs, show that the equation
$$4 x ^ { 2 } - 1 = \cot x$$
has only one root in the interval \(0 < x < \frac { 1 } { 2 } \pi\).
Verify by calculation that this root lies between 0.6 and 1 .
Use the iterative formula
$$x _ { n + 1 } = \frac { 1 } { 2 } \sqrt { } \left( 1 + \cot x _ { n } \right)$$
to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.