# Playing With Theta

Calculus Level 3

Let $$A(\theta )=\int { sin(\theta +\sin { \theta ){ e }^{ \cos { \theta } } } d\theta }$$

and $$B(\theta )=\int { cos(\theta +\sin { \theta ){ e }^{ \cos { \theta } } } d\theta }$$

Where $$A(0)=-1$$ and $$B(0)=0$$

Then find the value of the expression $$\frac { \ln { \left\{ { \left( A\left( \theta \right) \right) }^{ 2 }+{ \left( B\left( \theta \right) \right) }^{ 2 } \right\} } }{ \cos { \theta } }$$

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