Question:
If $\sin x=\frac{3}{5}$ and $0
Solution:
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, $\tan \frac{\mathrm{x}}{2}=\frac{1}{3}$