\frac{2tan{{30}^\circ}}{1+{tan{\ }}^2{30}^\circ} is equal to

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Solution

Q.
$\frac{2 t a n 30 °}{1 + {t a n}^{2} 30 °}$ is equal to

1 $\sin 60 °$

2 $\cos 60 °$

3 $\tan 60 °$

4 $\sin 30 °$

Ans.
(1)

We have,

$\frac{2 t a n 30 °}{1 + {t a n}^{2} 30 °} = \frac{2 \times \frac{1}{\sqrt{3}}}{1 + {(\frac{1}{\sqrt{3}})}^{2}} = \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}} = \frac{\frac{2}{\sqrt{3}}}{\frac{4}{3}} = \frac{2}{\sqrt{3}} \times \frac{3}{4} = \frac{\sqrt{3}}{2} = s i n 60 °$

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