Determine which of the following are trigonometric identities.
I. $\cot ( \theta ) \csc ( \theta ) = \sec ( \theta )$
II. $\cot ( \theta ) \sec ( \theta ) = \csc ( \theta )$
III. $\sec ( \theta ) \csc ( \theta ) = \cot ( \theta )$
IV. $\cot ( \theta ) \sin ( \theta ) = 1$
A) II and IV are the only identities.
B) II is the only identity.
C) III is the only identity.
D) I, III, and IV are the only identities.
E) I is the only identity.

Question

Quizplus · Accepted Answer

II is the only identity because $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$ and $\sec(\theta) = \frac{1}{\cos(\theta)}$, so $\cot(\theta) \sec(\theta) = \frac{\cos(\theta)}{\sin(\theta)} \cdot \frac{1}{\cos(\theta)} = \frac{1}{\sin(\theta)} = \csc(\theta)$.

Determine Which of the Following Are Trigonometric Identities cot⁡(θ)csc⁡(θ)=sec⁡(θ)\cot ( \theta ) \csc ( \theta ) = \sec ( \theta )cot(θ)csc(θ)=sec(θ)

Determine Which of the Following Are Trigonometric Identities $\cot ( \theta ) \csc ( \theta ) = \sec ( \theta )$