Question

Evaluate
2tan30°/1+tan2 30,°​

Answer 1

$= \frac{ 2\times \frac{1}{\sqrt{3}}}{ 1+ \Big( \frac{1}{\sqrt{3}}\Big)^{2}}$

• $\begin{gathered}= \frac{ \frac{2}{\sqrt{3}}}{ \frac{ 3+1}{3}} \\= \frac{ 2}{\sqrt{3}} \times \frac{3}{4} \\= \frac{\sqrt{3}}{2} \end{gathered}$

Therefore,

$\sf{Value \:of \: \frac{ 2tan 30 }{1 + tan^{2} 30\degree }}{= \frac{\sqrt{3}}{2} }$

Know More :-

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf \ Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

ThankYou (;