8. \( \cos \theta \cdot \csc \theta= \) a \( \cot \theta \) b \( \sin \theta \) c \( \tan \theta \) d \( \sec \theta \)

To simplify \( \cos \theta \cdot \csc \theta \), recall that \( \csc \theta = \frac{1}{\sin \theta} \). So, \( \cos \theta \cdot \csc \theta = \cos \theta \cdot \frac{1}{\sin \theta} = \frac{\cos \theta}{\sin \theta} \). This simplifies to \( \cot \theta \). Therefore, the correct answer is: a \( \cot \theta \). Understanding these fundamental trigonometric identities can enhance problem-solving, as they're interconnected! You can see how much of trigonometry relies on knowing conversions between functions—like knowing that \( \csc \theta \) is just the reciprocal of \( \sin \theta \). If you find yourself making mistakes, remember to keep the basic identities handy: \( \sin^2 \theta + \cos^2 \theta = 1 \), which can help you derive other relationships. It’s a great way to catch any missteps in solving trigonometric equations or identities—always double-check with this foundational truth!