যদি   $\tan{\alpha} - \tan{\beta} = p , \cot{\beta} - \cot{\alpha} = q , \alpha - \beta = \theta$   হয়,  তবে   $\cot{\theta}$   এর মান কত ?  

$\mathrm{p}=\tan \alpha-\tan \beta=\frac{\sin \alpha}{\cos \alpha}-\frac{\sin \beta}{\cos \beta}=\frac{\sin \alpha \cdot \cos \beta-\sin \beta \cdot \cos \alpha}{\cos \alpha \cdot \cos \beta}=\frac{\sin (\alpha-\beta)}{\cos \alpha \cdot \cos \beta} \Rightarrow \frac{1}{p}=\frac{\cos \alpha \cdot \cos \beta}{\sin (\alpha-\beta)}$ $q=\cot \beta-\cot \alpha=\frac{\cos \beta}{\sin \beta}-\frac{\cos \alpha}{\sin \alpha}=\frac{\sin \alpha \cdot \cos \beta-\cos \alpha \cdot \sin \beta}{\sin \alpha \cdot \sin \beta}=\frac{\sin (\alpha-\beta)}{\sin \alpha \cdot \sin \beta}$ $\therefore \frac{1}{p}+\frac{1}{q}=\frac{\cos (\alpha-\beta)}{\sin (\alpha-\beta)}=\cot (\alpha-\beta) ; \cot \theta=\frac{1}{p}+\frac{1}{q}$