Prove the Identity $$1 + \sec ^ { 2 } x \sin ^ { 2 } x = \sec ^ { 2 } x$$

question 44

Essay

Prove the identity.
- $$1 + \sec ^ { 2 } x \sin ^ { 2 } x = \sec ^ { 2 } x$$

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Definitions:

Consumer Surplus

The differential between the amount envisioned by consumers to pay for a good or service and the actual amount paid.

Perfectly Competitive

A market structure characterized by many buyers and sellers, free entry and exit, and a homogeneous product.

Consumer Surplus

The distinction between the ideal payment by consumers for a product or service and the financial outlay they make.

Average Cost

An alternative term for average total cost; the total cost divided by the quantity of output produced.