Question

\[\frac{1}{\cot \theta + \tan \theta}\] is equal to ______.

Options

• sin θ + cos θ

• sin θ. cos θ

• \[\frac{1}{\sin \theta \cdot \cos \theta}\]

• \[\frac{1}{\sin \theta + \cos \theta}\]

Answer 1

\[\frac{1}{\cot \theta + \tan \theta}\] is equal to sin θ. cos θ.

Explanation:

Solving,

\[\Rightarrow \frac{1}{\cot \theta + \tan \theta}\]

\[\Rightarrow \frac{1}{\frac{\cos \theta}{\sin \theta} + \frac{\sin \theta}{\cos \theta}}\]

\[\Rightarrow \frac{1}{\frac{\cos^2 \theta + \sin^2 \theta}{\cos \theta \cdot \sin \theta}}\]

\[\Rightarrow \frac{\cos \theta \cdot \sin \theta}{\cos^2 \theta + \sin^2 \theta}\]

Substituting, sin² θ + cos² θ = 1, we get:

⇒ sin θ. cos θ