Question 6 - A-Level Maths

Show that \(\cos ^ { 4 } x \equiv 1 - 2 \sin ^ { 2 } x + \sin ^ { 4 } x\).
Hence, or otherwise, solve the equation \(8 \sin ^ { 4 } x + \cos ^ { 4 } x = 2 \cos ^ { 2 } x\) for \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\).