If the product of the intercepts made by the straight line $\mathrm{xtan}\mathrm{\alpha }+\mathrm{ysec}\mathrm{\alpha }=1$ on the coordinates axes is equal to sin$\mathrm{\alpha }$ . Find $\mathrm{\alpha }$ .

$\text{ Given line }\mathrm{xtan}\mathrm{\alpha }+\mathrm{ysec}\mathrm{\alpha }=1$
$\frac{\mathrm{x}}{\cot \mathrm{\alpha }}+\frac{\mathrm{y}}{\cos \mathrm{\alpha }}=1$
$\mathrm{x}\text{-intercept}=\cot \mathrm{\alpha },\mathrm{y}\text{-intercepts }=\cos \mathrm{\alpha }$
Given that Product of intercepts=$\sin \alpha$
$\begin{array}{l}\Rightarrow \sin \mathrm{\alpha }=\cot \mathrm{\alpha }\cdot \cos \mathrm{\alpha }=\frac{\cos \mathrm{\alpha }}{\sin \mathrm{\alpha }}\cdot \cos \mathrm{\alpha }\\ \Rightarrow {\sin }^2\mathrm{\alpha }={\cos }^2\mathrm{\alpha }\\ \Rightarrow {\tan }^2\mathrm{\alpha }=1\\ \Rightarrow \mathrm{\alpha }=\frac{\mathrm{\pi }}{4}\end{array}$