যদি sinθ+cosecθ=2 হয়, তবে sinⁿθ+cosecⁿθ=?

$\begin{array}{l}\text {} \sin \theta+\operatorname{cosec} \theta=1 \Rightarrow \sin \theta+\frac{1}{\sin \theta}=1 \Rightarrow \sin ^{2} \theta+1=2 \sin \theta \\ \Rightarrow \sin ^{2} \theta+1-2 \sin \theta=0 \Rightarrow(\sin \theta-1)^{2}=0 \Rightarrow \sin \theta-1=0 \therefore \sin \theta=1 \\ \text { Now, } \sin ^{\mathrm{n}} \theta+\operatorname{cosec}^{\mathrm{n}} \theta=\sin ^{\mathrm{n}} \theta+\frac{1}{\sin ^{\mathrm{n}} \theta}=(1)^{\mathrm{n}}+\frac{1}{(1)^{\mathrm{n}}}=1+1=2\end{array}$