Determine Which of the Following Are Trigonometric Identities $\frac { \cos ( 4 x ) - \cos ( 2 x ) } { 2 \tan ( 3 x ) } = - \tan ( x )$

question 101

Multiple Choice

Determine which of the following are trigonometric identities.
$\frac { \cos ( 4 x ) - \cos ( 2 x ) } { 2 \tan ( 3 x ) } = - \tan ( x )$
$\frac { \cos ( 3 x ) - \cos ( x ) } { \sin ( 3 x ) - \sin ( x ) } = - \tan ( 2 x )$
$\frac { \cos ( 6 x ) - \cos ( 2 x ) } { \sin ( 4 x ) + \sin ( 2 x ) } = - \tan ( 3 x$

• A) II is the only identity.
• B) I is the only identity.
• C) I, II, and III are identities.
• D) None are identities.
• E) I and III are the only identities.

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Definitions:

Main Connective

In logic, the operator (such as AND, OR, NOT) that determines the truth value of a complex sentence based on the truth values of its components.

Tautology

A statement or proposition that is true by necessity or by virtue of its logical form, often repeating the same idea in different words.

Main Connective

In a logical formula, the operator that holds the highest precedence, determining the formula's overall truth value.

Truth Values

The valuation of a statement in logic that indicates its truthfulness, typically classified as either true or false.