MCQ
$\frac{2 \tan 30^{\circ}}{1+\tan ^2 30^{\circ}}$ is equal to
- ✓$\sin 60^{\circ}$
- B$\cos 60^{\circ}$
- C$\tan 60^{\circ}$
- D$\sin 30^{\circ}$
✓
Answer
Correct option: A.
$\sin 60^{\circ}$
(A)$\sin 60^{\circ}$
$
\text {} \frac{2 \tan 30^{\circ}}{1+\tan ^2 30^{\circ}}=\frac{2 \times \frac{1}{\sqrt{3}}}{1+\left(\frac{1}{\sqrt{3}}\right)^2}=\frac{\frac{2}{\sqrt{3}}}{1+\frac{1}{3}}=\frac{2}{\sqrt{3}} \times \frac{3}{4}=\frac{\sqrt{3}}{2}=\sin 60^{\circ}
$
$
\text {} \frac{2 \tan 30^{\circ}}{1+\tan ^2 30^{\circ}}=\frac{2 \times \frac{1}{\sqrt{3}}}{1+\left(\frac{1}{\sqrt{3}}\right)^2}=\frac{\frac{2}{\sqrt{3}}}{1+\frac{1}{3}}=\frac{2}{\sqrt{3}} \times \frac{3}{4}=\frac{\sqrt{3}}{2}=\sin 60^{\circ}
$
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