5 It is given that \(\sin A = \frac { \sqrt { 5 } } { 3 }\) and \(\sin B = \frac { 1 } { \sqrt { 5 } }\), where the angles \(A\) and \(B\) are both acute.
- Show that the exact value of \(\cos B = \frac { 2 } { \sqrt { 5 } }\).
- Hence show that the exact value of \(\sin 2 B\) is \(\frac { 4 } { 5 }\).
- Show that the exact value of \(\sin ( A - B )\) can be written as \(p ( 5 - \sqrt { 5 } )\), where \(p\) is a rational number.
- Find the exact value of \(\cos ( A - B )\) in the form \(r + s \sqrt { 5 }\), where \(r\) and \(s\) are rational numbers.