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} $