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 \( \cos \theta \) is \( \sec \theta \) and the reciprocal of \( \sin \theta \) is \( \csc \theta \).

Answer 1

The Correct Option is C

Using trigonometric identities:
\[ \sin \theta \times \cot \theta = \sin \theta \times \frac{\cos \theta}{\sin \theta} = \cos \theta. \] The reciprocal is:
\[ \frac{1}{\cos \theta} = \sec \theta. \]