Prove the Identity $$\frac { 5 \csc ^ { 2 } x + 4 \csc x - 1 } { \cot ^ { 2 } x } = \frac { 5 \csc x - 1 } { \csc x - 1 }$$

question 143

Essay

Prove the identity.
- $$\frac { 5 \csc ^ { 2 } x + 4 \csc x - 1 } { \cot ^ { 2 } x } = \frac { 5 \csc x - 1 } { \csc x - 1 }$$

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Definitions:

Diseconomies of Scale

Increased costs per unit that occur when a company grows too large, leading to inefficiencies.

Long-Run Average Cost Curve

A graphical representation showing the minimum cost per unit at which a firm can produce any given level of output in the long run when all inputs are variable.

Diseconomies of Scale

The phenomenon where, as a firm becomes too large, its costs per unit increase due to inefficiencies, leading to a decrease in overall productivity or cost-effectiveness.

Long-Run Average Cost Curve

A graphical representation used in economics to show the lowest average cost of production at which any given level of output can be produced in the long run, when all inputs are variable.