Let's evaluate each of the statements regarding trigonometric identities to determine which are true.
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tangent (θ) = cosine (θ) / sine (θ): This statement is false. The correct identity is: \[ \tan(θ) = \frac{\sin(θ)}{\cos(θ)} \]
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cotangent (θ) = cosine (θ) / sine (θ): This statement is true. The cotangent is defined as: \[ \cot(θ) = \frac{\cos(θ)}{\sin(θ)} \]
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secant (θ) = 1 / sine (θ): This statement is false. The correct identity is: \[ \sec(θ) = \frac{1}{\cos(θ)} \]
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cosecant (θ) = 1 / cosine (θ): This statement is false. The correct identity is: \[ \csc(θ) = \frac{1}{\sin(θ)} \]
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secant (θ) = tangent (θ) / sine (θ): This statement is also false. The correct relationship is: \[ \sec(θ) = \frac{1}{\cos(θ)} \quad \text{and} \quad \tan(θ) = \frac{\sin(θ)}{\cos(θ)} \]
Thus, the only true statement from the options provided is:
- cotangent (θ) = cosine (θ) / sine (θ).