A Trigo limit (1)

Calculus Level 3

\[L=\large\lim _{ x\rightarrow 0 }{ \left ( \cos { \left( \frac { \pi }{ 4 } +x \right) \sec { \left( \frac { \pi }{ 4 } -x \right) } } \right ) } ^{ \frac { 1 }{ x } }\]

For \(L\) as defined above, what is \(\ln { \left( \frac { 1 }{ L } \right) } \)?

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