Prove each of the following identities :
`(cos^(3) theta + sin^(3) theta)/(cos theta + sin theta ) + (cos^(3) theta - sin^(3) theta)/(cos theta - sin theta ) = 2 `

Explanation

To prove the identity

\[ \frac{\cos^3 \theta + \sin^3 \theta}{\cos \theta + \sin \theta} + \frac{\cos^3 \theta - \sin^3 \theta}{\cos \theta - \sin \theta} = 2 \]

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

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