Trig1.10

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Simplify $\frac{\sin^3\theta+\cos^3\theta}{\sin\theta+\cos\theta}\,$

Given that $\frac{\sin^3\theta+\cos^3\theta}{\sin\theta+\cos\theta}\,$

Simplifying we get

$\frac{(\sin\theta+\cos\theta)(\sin^2 \theta-\sin\theta \cos\theta+\cos^2 \theta)}{\sin\theta+\cos\theta}\,$

$\sin^2 \theta+\cos^2 \theta-\sin\theta \cos\theta\,$

$1-\sin\theta \cos\theta\,$

which is the simplest form.

Main Page:Trigonometry

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