Connect the curve 5

Calculus Level 2

The curve of $$\sin { \left( ax \right) }$$ is tangent to the curve of $$\sin { \left( x \right) }$$ at $$x=\frac { 5\pi }{2 }$$.

If minimum positive value of $$a$$ can be expressed as $$\frac { A }{B }$$ for co-prime $$A$$ and $$B$$, then find $$A+B$$.

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