Prove the Identity $$( \sin x ) ( \tan x \cos x - \cot x \cos x ) = 1 - 2 \cos ^ { 2 } x$$

question 15

Essay

Prove the identity.
- $$( \sin x ) ( \tan x \cos x - \cot x \cos x ) = 1 - 2 \cos ^ { 2 } x$$

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Definitions:

Harem

A social structure in some species where one male mates with multiple females, excluding other males from mating with them.

Resource Defense Polygyny

A mating system in which males acquire and defend territories rich in resources that are attractive to females.

Grevy's Zebras

A species of zebra distinguished by its large ears and narrow stripes, known for its conservation status and social behavior.

Water Sources

Locations or objects from which water can be obtained, including natural sources like rivers and lakes or man-made systems.