Question

\[\frac{\sin A \tan A}{1 - \cos^2 A}\] is equal to:

Options

• cos A

• sec A

• cosec A

• sin A

Answer 1

sec A

Explanation:

Solving,

\[\Rightarrow \frac{\sin A \tan A}{1 - \cos^2 A}\]

\[\Rightarrow \frac{\sin A \tan A}{\sin^2 A}\]

\[\Rightarrow \frac{\tan A}{\sin A}\]

\[\Rightarrow \frac{\frac{\sin A}{\cos A}}{\sin A}\]

\[\Rightarrow \frac{\sin A}{\sin A \times \cos A}\]

\[\Rightarrow \frac{1}{\cos A}\]

\[\Rightarrow \sec A\]