Question

If $\tan \frac{A}{2}=\frac{3}{2}$ then the value of $\frac{1-\cos A}{1+\cos A}$ is

• A. $-5$
• B. $5$
• C. $9/4$
• D. $4/9$

Answer 1

The correct option is C $9/4$

Given $\tan \frac{A}{2}=\frac{3}{2}$

$\frac{1-\cos A}{1+\cos A}=\frac{2{\sin }^2\frac{A}{2}}{2{\cos }^2\frac{A}{2}}$

$={\tan }^2\frac{A}{2}$

$=(\frac{3}{2}{)}^2$

$=\frac{9}{4}$