# "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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