Prove the following identities: `(sin^3theta+cos^3theta)/(sintheta+costheta)+sinthetacostheta=1`

Explanation

To prove the identity

\[ \frac{\sin^3 \theta + \cos^3 \theta}{\sin \theta + \cos \theta} + \sin \theta \cos \theta = 1, \]

we will start from the left-hand side (LHS) and simplify it step by step.

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