$\sin \alpha+\operatorname{cosec} \alpha=2$ হলে, $\sin ^{n} \alpha+\operatorname{cosec}^{n} \alpha$ এর মান-

$\sin \alpha+\operatorname{cosec} \alpha$ $=2$ $\Rightarrow \sin \alpha+\frac{1}{\sin \alpha}$ $=2$ $\Rightarrow \sin ^{2} \alpha+1$ $=2 \sin \alpha$ $\Rightarrow \sin ^{2} \alpha-2 \sin \alpha+1=$ $0$ $\Rightarrow(\sin \alpha-1)^{2}=0$ $\Rightarrow \sin \alpha=1$ এবং $\operatorname{cosec} \alpha=1$ $\therefore \sin ^{\mathrm{n}} \alpha+\operatorname{cosec}^{\mathrm{n}} \alpha$ $=1^{\mathrm{n}}+\mathrm{1}^{\mathrm{n}}$ $=1+1=2$