$\tan \theta+\sec \theta=x$ হলে $\operatorname{cosec} \theta$ এর মান কত

$\tan \theta+\sec \theta=x$ $\Rightarrow \frac{\sin \theta}{\cos \theta}+\frac{1}{\cos \theta}=x$ $\Rightarrow \frac{(\sin \theta+1)^{2}}{\cos ^{2} \theta}=\mathrm{x}^{2}$ $\Rightarrow \frac{(\sin \theta+1)^{2}}{\cos ^{2} \theta}=\mathrm{x}^{2}$ $\Rightarrow \frac{(1+\sin \theta)^{2}}{1-\sin ^{2} \theta}=\mathrm{x}^{2}$ $\Rightarrow \frac{1+\sin \theta}{1-\sin \theta}$ $=\mathrm{x}^{2}$ $\Rightarrow \frac{1+\sin \theta+1-\sin \theta}{1+\sin \theta-1+\sin \theta}=\frac{\mathrm{x}^{2}+1}{\mathrm{x}^{2}-1}$ $\Rightarrow \frac{2}{2 \sin \theta}$ $=\frac{\mathrm{x}^{2}+1}{\mathrm{x}^{2}-1}$ $\therefore \operatorname{cosec} \theta$ $=\frac{\mathrm{x}^{2}+1}{\mathrm{x}^{2}-1}$ $\therefore \sin \theta$ $=\frac{\mathrm{x}^{2}-1}{\mathrm{x}^{2}+1}$