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

Question

Quizplus · Accepted Answer

II and IV are true identities. II is true because $\csc(\theta) = \frac{1}{\sin(\theta)}$ and $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$, so $\csc(\theta)\tan(\theta) = \frac{1}{\sin(\theta)} \cdot \frac{\sin(\theta)}{\cos(\theta)} = \frac{1}{\cos(\theta)} = \sec(\theta)$. IV is true because $\csc(\theta) = \frac{1}{\sin(\theta)}$, so $\csc(\theta)\sin(\theta) = 1$.

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

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