Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

$\begin{array}{rl}& \alpha =\sum _{\mathrm{r}-30}^{59}\frac{1}{\sin (2\mathrm{r}{)}^{\circ }\sin (2\mathrm{r}+1{)}^{\circ }}\\ & \frac{\alpha }{\mathrm{cosec}{1}^{\circ }}=\sum _{\mathrm{r}-30}^{59}\frac{\sin 1^{\circ }}{\sin (2\mathrm{r}{)}^{\circ }\sin (2\mathrm{r}+1{)}^{\circ }}\\ & =\sum _{\mathrm{r}-30}^{59}\left(\cot (2\mathrm{r}{)}^{\circ }-\cot (2\mathrm{r}+1{)}^{\circ }\right)\\ & =\cot 60^{\circ }-\cot 61^{\circ }\\ & +\cot 62^{\circ }-\cot 63^{\circ }\\ & ⋮\\ & +\cot \left(118^{\circ }\right)-\cot \left(119^{\circ }\right)\\ & \frac{\alpha }{\mathrm{cosec}{1}^{\circ }}=\cot 60^{\circ }=\frac{1}{\sqrt{3}}\\ & {\left(\frac{\mathrm{cosec}{1}^{\circ }}{\alpha }\right)}^2=3\end{array}$