5 Given the equation \(\sin \left( x + 45 ^ { \circ } \right) = 2 \cos x\), show that \(\sin x + \cos x = 2 \sqrt { 2 } \cos x\).
Hence solve, correct to 2 decimal places, the equation for \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\).