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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
Question
$\frac{{2\tan 30^\circ }}{{1 + {{\tan }^2}30^\circ }} = $
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Answer

Given: $\frac{{2\tan 30^\circ }}{{1 + {{\tan }^2}30^\circ }}$
= $\frac{{2 \times \frac{1}{{\sqrt 3 }}}}{{1 + {{\left( {\frac{1}{{\sqrt 3 }}} \right)}^2}}}$
= $\frac{2}{{\sqrt 3 \left( {\frac{{3 + 1}}{3}} \right)}}$
= $\frac{6}{{4\sqrt 3 }} = \frac{3}{{2\sqrt 3 }}$
= $\frac{{\sqrt 3 }}{2}$
= $\sin {60^ \circ }$

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