Calciferous Cosine

Geometry Level 2

\[ \large \cos { \left( \frac { \pi }{ 4 } +x \right) } +\cos { \left( \frac { \pi }{ 4 } -x \right) } =a\]

\[ \large \cos { \left( \frac { 3\pi }{ 4 } +x \right) } -\cos { \left( \frac { 3\pi }{ 4 } -x \right) } =b\]

\({ a }^{ 2 }+{ b }^{ 2 }=\ ?\)

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