...with a beak and feathers...

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