Question

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

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

Answer 1

Answer: (A)

sin 60°

Answer 2

sin 30°
$= \frac{2 × \left(\frac{1}{\sqrt3}\right)}{1 + \left(\frac{1}{\sqrt3}\right)^2}$

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

$= \frac{\frac{2}{\sqrt3} }{ \frac{4}{3}}$

$=\frac{ 6}{4\sqrt3}$

$= \frac{\sqrt3}{2}$

Out of the given alternatives, only sin 60° $= \frac{\sqrt3}{2}$
Hence, (A) is correct.