What is the reciprocal of sinθ × cotθ ?

Question

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

(A) \(\tan \theta\)

(B) \(\cos \theta\)

(C) \(\sec \theta\)

(D) \(\text {cosec } \theta\)

Answer 1

Correct option is (C) \(\sec \theta\)

\(\sin \theta \times \cot \theta \)

\(= \sin \theta \times \frac{\cos \theta}{\sin \theta}\quad\left[\because \cot \theta=\frac{\cos \theta}{\sin \theta}\right] \)

\(= \cos \theta\)

The reciprocal of \(\cos \theta\) is

\(=\frac{1}{\cos \theta} \quad\left[\because \cos \theta=\frac{1}{\sec \theta}\right]\)

\(=\sec \theta\)