4 Angle \(x\) is such that \(\sin x = a + b\) and \(\cos x = a - b\), where \(a\) and \(b\) are constants.
- Show that \(a ^ { 2 } + b ^ { 2 }\) has a constant value for all values of \(x\).
- In the case where \(\tan x = 2\), express \(a\) in terms of \(b\).