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Calculus Level 4

Consider the graphs of $$\sin x +\cos x$$ and $$\sin x -\cos x$$

Let the area of a rectangle that encloses one of the areas formed between the curves be $$R$$

If the minimum of $$R$$ be $$a+b\pi$$, where $$a,b$$ are positive integers, find $$a+b$$

This is part of the Sinusoidal, Cosinusoidal series

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