Can We Compound The Range?

Geometry Level 2

\[ | \sin x | \leq 1 \qquad \qquad | \cos x | \leq 1 \]

We know that for all real numbers \(x\), the inequalities above are true. What is the smallest possible value of \(R\) satisfying

\[ | \sin x + \cos x | \leq R ? \]

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