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CBSE · Class 10 · Mathematics · Introduction to TrigonometryWhat is the value of $\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ}$?

Step-by-Step Solution

Substitute $\tan 30^\circ = \frac{1}{\sqrt{3}}$ into the expression: $\frac{2(1/\sqrt{3})}{1 + (1/\sqrt{3})^2} = \frac{2/\sqrt{3}}{1 + 1/3} = \frac{2/\sqrt{3}}{4/3} = \frac{2}{\sqrt{3}} \times \frac{3}{4} = \frac{6}{4\sqrt{3}} = \frac{\sqrt{3}}{2}$. Since $\sin 60^\circ = \frac{\sqrt{3}}{2}$, the correct option is $\sin 60^\circ$.

Detailed Options Breakdown
Option : $\sin 60^\circ$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 1: $\cos 60^\circ$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.

Option 2: $\tan 60^\circ$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.

Option 3: $\sin 30^\circ$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.

💡 Study Guide: This question tests core syllabus concepts from Introduction to Trigonometry. For formulas, key summaries, and mock exam reference guides, read the full Introduction to Trigonometry Revision Notes.
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