Prove the Identity $\cos 3 x=\cos ^{3} x-3 \sin ^{2} x \cos x$

question 10

Essay

Prove the identity:
$\cos 3 x=\cos ^{3} x-3 \sin ^{2} x \cos x$

Understand the role and importance of endosymbionts in insect nutrition.

Grasp the evolutionary trade-offs between replication within hosts and transmission between hosts for parasites/pathogens.

Comprehend how endogenous retroviruses and mobile genetic elements have coevolved with their host genomes.

Differentiate between parasitic and mutualistic relationships in the context of mobile genetic elements.

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Definitions:

Nationalized

Refers to industries or assets that have been transferred from private to government ownership.

Best Interest

A principle that guides decisions by prioritizing the benefits and welfare of those affected over other considerations.

Society

A community of individuals living together and interacting under shared norms, values, and institutions.

Profit Maximizes

The technique a firm uses to determine the most profitable price and quantity of production.