# The Maximized Slope

Calculus Level 5

Let function $$f$$ be defined as $$f(x)=(\cos(a))^x+(\sin(a))^x$$ where $$a$$ is a parameter that is constantly changing within the interval $$0<a<\frac{\pi}{2}$$.

The $$y$$-intercept's tangent line is maximized when the value of $$a$$ reaches a certain value.

If the value of the maximized slope is expressed as $$\ln($$$$\frac{m}{n}$$$$)$$ where $$m$$ and $$n$$ are coprime integers, find the value of $$m+n$$.

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