Prove the Identity $$\cos 4 x + \cos 2 x = 2 - 2 \sin ^ { 2 } 2 x - 2 \sin ^ { 2 } x$$

question 114

Essay

Prove the identity.
- $$\cos 4 x + \cos 2 x = 2 - 2 \sin ^ { 2 } 2 x - 2 \sin ^ { 2 } x$$

---

Definitions:

Variable Selling Expenses

Selling costs that fluctuate with sales volume, such as commissions for sales staff.

Break-Even Sales

The amount of revenue required to cover all fixed and variable expenses, resulting in zero profit.

Variable Expenses

Expenses that vary directly with the level of production or sales, such as raw materials and direct labor costs.

Fixed Expenses

Costs that do not fluctuate with the level of production or sales, including rent, salaries, and insurance premiums.