Prove the Identity $$\sec ^ { 4 } x - \tan ^ { 4 } x = \sec ^ { 2 } x + \tan ^ { 2 } x$$

question 142

Essay

Prove the identity.
- $$\sec ^ { 4 } x - \tan ^ { 4 } x = \sec ^ { 2 } x + \tan ^ { 2 } x$$

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Definitions:

Marginal Physical Product

The additional output resulting from using one more unit of a physical input, holding other inputs constant, in the production process.

Total Revenue

The price of a good or service multiplied by the number of units sold.

Marginal Revenue Product

The additional revenue generated from employing one more unit of a resource, factor of production, or input.

Perfect Competition

An industry with so many firms that no one firm has any influence over price, and firms produce an identical product.