(1,1), (cosα, sinα) ও (secα, cosecα) সমরেখ হলে, α=কত?

$\begin{array}{l} \Rightarrow \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y_{3}-y_{1}}{x_{3}-x_{1}} \\ \Rightarrow \frac{\sin \alpha-1}{\cos \alpha-1}=\frac{\operatorname{cosec} \alpha-1}{\sec \alpha-1} \\ \Rightarrow \frac{\sin \alpha-1}{\cos \alpha-1}=\frac{\cos \alpha(1-\sin \alpha)}{\sin \alpha(1-\cos \alpha)} \Rightarrow\left(\frac{\sin \alpha-1}{\cos \alpha-1}\right) * \frac{\cos \alpha(\sin \alpha-1)}{\sin \alpha(\cos \alpha-1)}=0 \\ \Rightarrow \frac{(\sin \alpha-1)}{(\cos \alpha-1)}(1 * \cot \alpha)=0 \end{array}$

Now, $1-\cot \alpha=0$

$\cot \alpha=1$

$\therefore \alpha=45^{\circ}$