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

Answer: (C)

tan 60°

Answer 2

$\frac{2\ tan\ 30°}{1 - tan^2 30°}$

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

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

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

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

Hence, option (C) is correct.