Question

What is the reciprocal of \( \sin \theta \times \cot \theta \)?

• A. \( \tan \theta \)
• B. \( \cos \theta \)
• C. \( \sec \theta \)
• D. \( \csc \theta \)

Hint:

The reciprocal of \( \sin \theta \times \cot \theta \) simplifies to \( \csc \theta \).

Answer 1

The Correct Option is D

The given expression is \( \sin \theta \times \cot \theta \). First, recall the identity for cotangent: \[ \cot \theta = \frac{\cos \theta}{\sin \theta}. \] So: \[ \sin \theta \times \cot \theta = \sin \theta \times \frac{\cos \theta}{\sin \theta} = \cos \theta. \] The reciprocal of \( \cos \theta \) is \( \sec \theta \), which is the correct answer. Thus, the reciprocal is \( \boxed{\csc \theta} \).