Determine which of the following are trigonometric identities. I. $\sin ( \theta ) + \cot ( \theta ) \cos ( \theta ) = \csc ( \theta )$
II. $\cot ( \theta ) - \sin ( \theta ) \cos ( \theta ) = 0$
III. $\sin ( \theta ) + \sin ( \theta ) \cos ( \theta ) = \csc ( \theta )$
A) I is the only identity.
B) I and II are the only identities.
C) III is the only identity.
D) I, II, and III are identities.
E) II is the only identity.

Question

Quizplus · Accepted Answer

I is a true identity because $\sin(\theta) + \cot(\theta)\cos(\theta) = \sin(\theta) + \frac{\cos(\theta)}{\sin(\theta)}\cos(\theta) = \sin(\theta) + \frac{\cos^2(\theta)}{\sin(\theta)} = \sin(\theta) + \frac{1-\sin^2(\theta)}{\sin(\theta)} = \frac{\sin(\theta)}{\sin(\theta)} = \csc(\theta)$. II and III are not identities because they do not hold for all values of $\theta$.

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

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