Solve this

Given: $\sin x=\frac{3}{5}$ and $0

To Find: $\tan \frac{X}{2}$

Formula used:

$\tan \frac{x}{2}=\frac{\sin x}{1+\cos x}$

Now, $\cos x=\sqrt{1-\sin ^{2} x}(\because \cos x$ is positive in I quadrant)

$\Rightarrow \cos x=\sqrt{1-\left(\frac{3}{5}\right)^{2}}=\sqrt{1-\frac{9}{25}}=\frac{4}{5}$

Since, $\tan \frac{x}{2}=\frac{\sin x}{1+\cos x}=\frac{\frac{3}{5}}{1+\frac{4}{5}}=\frac{3}{5} \times \frac{5}{9}=\frac{1}{3}$

Hence, $\tan \frac{\mathrm{x}}{2}=\frac{1}{3}$