Step 1: Given that:

We need to Determine whether the statement, "The word identity is used in different ways in additive identity, multiplicative identity, and trigonometric identity". makes sense or does not make sense.

Step 2: Definition Used:

A mathematically acceptable statement is any declarative sentence that is either true or false but not both.

The word Identity is used in different ways along with several words to give the identity of those functions. However, Identity means Uniqueness.

Step 3: Explanation And Reasoning:

Additive Identity: Yes the word additive identity makes a sense, Additive identity states that anything, when added to the function, will not affect the function, the function remains the same. However, 0 is the additive identity used in mathematics.

For example:

a+0=0+a=a

Multiplicative Identity:

Yes, the word multiplicative identity makes a sense, Multiplicative identity states that anything, when Multiplied to the function, will not affect the function, the function remains the same. However, 1 is the Multiplicative identity used in mathematics.

For example:

ax1=1xa=a

Trigonometric Identity:

Yes, the word Trigonometric identity makes a sense, Trigonometric identity refers to some basic formulae of Trigonometric Used to perform actions in problems based on trigonometry.

For example:

\(\displaystyle{{\sin}^{2}{x}}+{{\cos}^{2}{x}}={1}\)

\(\displaystyle{{\sec}^{2}{x}}-{{\tan}^{2}{x}}={1}\)

\(\displaystyle \cos{{e}}{c}^{2}{x}-{{\cot}^{2}{x}}={1}\)

We need to Determine whether the statement, "The word identity is used in different ways in additive identity, multiplicative identity, and trigonometric identity". makes sense or does not make sense.

Step 2: Definition Used:

A mathematically acceptable statement is any declarative sentence that is either true or false but not both.

The word Identity is used in different ways along with several words to give the identity of those functions. However, Identity means Uniqueness.

Step 3: Explanation And Reasoning:

Additive Identity: Yes the word additive identity makes a sense, Additive identity states that anything, when added to the function, will not affect the function, the function remains the same. However, 0 is the additive identity used in mathematics.

For example:

a+0=0+a=a

Multiplicative Identity:

Yes, the word multiplicative identity makes a sense, Multiplicative identity states that anything, when Multiplied to the function, will not affect the function, the function remains the same. However, 1 is the Multiplicative identity used in mathematics.

For example:

ax1=1xa=a

Trigonometric Identity:

Yes, the word Trigonometric identity makes a sense, Trigonometric identity refers to some basic formulae of Trigonometric Used to perform actions in problems based on trigonometry.

For example:

\(\displaystyle{{\sin}^{2}{x}}+{{\cos}^{2}{x}}={1}\)

\(\displaystyle{{\sec}^{2}{x}}-{{\tan}^{2}{x}}={1}\)

\(\displaystyle \cos{{e}}{c}^{2}{x}-{{\cot}^{2}{x}}={1}\)