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8. Introduction to Trigonometry
medium
$\frac{2 \tan 30^{\circ}}{1+\tan ^{2} 30^{\circ}}=$
A
$\cos 60^{\circ}$
B
$\sin 60^{\circ}$
C
$\tan 60^{\circ}$
D
$\sin 30^{\circ}$
Solution
$\frac{2 \tan 30^{\circ}}{1+\tan ^{2} 30^{\circ}}$
$=\frac{2\left(\frac{1}{\sqrt{3}}\right)}{1+\left(\frac{1}{\sqrt{3}}\right)^{2}}=\frac{\frac{2}{\sqrt{3}}}{1+\frac{1}{3}}=\frac{\frac{2}{\sqrt{3}}}{\frac{4}{3}}$
$=\frac{6}{4 \sqrt{3}}=\frac{\sqrt{3}}{2}$
Out of the given alternatives, only $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$
Standard 10
Mathematics
