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Introduction to Trigonometry · Class 10 · CBSE Mathematics

The value of frac{2 tan 30^circ}{1 + tan^2 30^circ} is equal to:

Practice question from Introduction to Trigonometry (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-EA0DB6

The value of 2tan⁡30∘1+tan⁡230∘\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ} is equal to:

  1. A.sin⁡60∘\sin 60^\circCorrect answer
  2. B.cos⁡60∘\cos 60^\circ
  3. C.tan⁡60∘\tan 60^\circ
  4. D.sin⁡30∘\sin 30^\circ

Solution

Substitute tan⁡30∘=13\tan 30^\circ = \frac{1}{\sqrt{3}}. The expression becomes 2(1/3)1+(1/3)2=2/31+1/3=2/34/3=23×34=32\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{\sqrt{3}}{2}. Since sin⁡60∘=32\sin 60^\circ = \frac{\sqrt{3}}{2}, the correct option is A.

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