Question

Choose the correct option and justify your choice: \(\frac{2\ tan\ 30°}{1 - tan^2 30°} =\)

• A. cos 60°
• B. sin 60°
• C. tan 60°
• D. sin 30°

Answer 1

The Correct Option is C

\(\frac{2\ tan\ 30°}{1 - tan^2 30°}\)

\(=\frac{ 2 × \left(\frac{1}{\sqrt3}\right) }{ 1 - \left(\frac{1}{\sqrt3}\right)^2}\)

\(= \frac{\left(\frac{2}{\sqrt3}\right) }{ \left(1 - \frac{1}{3}\right)}\)

\(= \frac{\left(\frac{2}{\sqrt3}\right) }{ \left(\frac{2}{3}\right)}\)

\(= \sqrt3\)
Out of the given option only tan 60° \(= \sqrt3\).

Hence, option (C) is correct.