Prove the Identity $\frac{\sin ^{3} A-\cos ^{3} A}{\sin ^{2} A-\cos ^{2} A}=\frac{2+\sin 2 A}{2(\sin A+\cos A)}$

question 21

Essay

Prove the identity:
$\frac{\sin ^{3} A-\cos ^{3} A}{\sin ^{2} A-\cos ^{2} A}=\frac{2+\sin 2 A}{2(\sin A+\cos A)}$

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Definitions:

Operating Lease

A lease agreement for equipment or property that does not transfer ownership to the lessee and is typically for a period shorter than the asset's useful life.

Total Expense

The sum of all expenses incurred by a business, including cost of goods sold, operating expenses, and non-operating expenses.

Manufacturing Profit

The profit earned from the manufacturing operations after deducting the costs associated with the production of goods.

Inventory Cost

The total cost incurred to procure, produce, and store unsold goods, including raw materials, labor, and overhead expenses.