Simplify the following. $$\frac{sin³A - cos^3 A}{sin A - cos A}$$​where A is an acute angle.

Correct option is A

Given:

​$$\frac {sin^3 A- cos^3A}{sinA-cosA}$$​​

Formula Used:

​$$sin^2A+cos^2A = 1$$​​

Solution:

​$$=\frac {sin^3A-cos^3A}{sinA-cosA}\\ \ \\ = \frac{\cancel{ (\sin A - \cos A)}(\sin^2 A + \cos^2 A +\sin A \cdot \cos A)}{\cancel{(\sin A -\cos A)}} \\ \ \\ = \sin^2 A + \cos^2 A +\sin A \cdot \cos A \\ \ \\ = 1+sin A \cdot \cos A$$​​

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