"Series" feat. "Trigonometry"

Algebra Level 3

The first \(2\) terms of an arithmetic progression are \(1\) and \(\cos^2 x\) respectively. The sum of the first \(10\) terms of the series, \(S_{10}\) ,can be written as \(a-b\sin^2 x\) where \(a\) and \(b\) are integers. Find \(a+b\).

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