$\operatorname{cosec} \theta=\frac{13}{5}$ এবং $\frac{\pi}{2}<\theta<\pi$ এর মান নিচের কোনটি হবে ?

$\operatorname{cosec} \theta=\frac{13}{5} \Rightarrow \operatorname{cosec}^{2} \theta=\frac{169}{25}$ $\begin{array}{l}\Rightarrow 1+\cot ^{2} \theta=\frac{169}{25} \\\Rightarrow \cot ^{2} \theta=\frac{169}{25}-1=\frac{169-25}{25}=\frac{144}{25} \\\Rightarrow \cot \theta= \pm \frac{12}{5} \Rightarrow \tan \theta= \pm \frac{5}{12}\end{array}$ $\frac{\pi}{2}<\theta<\pi$ ব্যবধিতে $\tan \theta=-\frac{5}{12}$