Question

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

Answer 1

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

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

$=1-\sin \theta \cos \theta +\sin \theta \cos \theta$

$=1$