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)

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