Inspired by Sandeep Bhardwaj problem

Geometry Level 4

\[\large f(x) = \dfrac{\sin(x) + \sin(3x) + \sin(5x) + \ldots + \sin(40103x)}{\cos(x) + \cos(3x) + \cos(5x) + \ldots + \cos(40103x)}\]

Fundamental period of \(f(x)\) can be represented as \(\dfrac{a\pi}{b}\), where \(a, b \) are coprime numbers. Find \( a + b \).

Inspiration

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