Prove the following identity: `(sin^3A+cos^3A)/(sinA+cosA)+(sin^3A-cos^3A)/(sinA-cosA)=2`

Explanation

To prove the identity

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

we will use the algebraic identities for the sum and difference of cubes.

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