Question

\(\frac{2\,tan\,30^0}{1-tan^2\,30^0}=\)

• A. sin 60°
• B. cos 60°
• C. tan 60°
• D. cot 60°

Answer 1

The Correct Option is C

Step 1: Recall the double-angle identity for tangent.

The double-angle identity for tangent is:

\[ \tan(2\theta) = \frac{2\tan\theta}{1 - \tan^2\theta} \]

Here, \( \theta = 30^\circ \), so:

\[ \frac{2\tan 30^\circ}{1 - \tan^2 30^\circ} = \tan(2 \cdot 30^\circ) = \tan 60^\circ \]

Step 2: Simplify \( \tan 60^\circ \).

From trigonometric values, we know:

\[ \tan 60^\circ = \sqrt{3} \]

The expression simplifies to \( \tan 60^\circ \), which corresponds to option \( \mathbf{(3)} \).

Final Answer: The value of \( \frac{2\tan 30^\circ}{1 - \tan^2 30^\circ} \) is \( \mathbf{\tan 60^\circ} \), which corresponds to option \( \mathbf{(3)} \).