What is \frac{\sin^{3}\theta+\cos^{3}\theta}{\sin\theta+\cos\theta}+\frac{\sin^{3}\theta-\cos^{3}\theta}{\sin\theta-\cos\theta} equal to?

Explanation

Using the identities a^3 \pm b^3 = (a \pm b)(a^2 \mp ab + b^2), the expression simplifies to (\sin^2\theta - \sin\theta\cos\theta + \cos^2\theta) + (\sin^2\theta + \sin\theta\cos\theta + \cos^2\theta) = 2(\sin^2\theta + \cos^2\theta) = 2.

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