Question

If $\tan \frac{\theta }{2}=\frac{1}{2}$, then the value of $\sin \theta$ is

• A. $\frac{4}{5}$
• B. $\frac{3}{5}$
• C. $\frac{1}{2}$
• D. $1$
• E. $\frac{2}{5}$

Answer 1

Answer: (A)

$\frac{4}{5}$

Given, $\tan \frac{\theta }{2}=\frac{1}{2}$

We know $\sin \theta =\frac{2\tan \frac{\theta }{2}}{1+{\tan }^2\frac{\theta }{2}}=\frac{2\times \frac{1}{2}}{1+{\left(\frac{1}{2}\right)}^2}$
$=\frac{1}{1+\frac{1}{4}}=\frac{1}{\left(\frac{5}{4}\right)}$

$=\frac{4}{5}$