[tex]ctgx=6\Rightarrow (ctgx)^{2}=36\Rightarrow (\frac{\cos{x}}{\sin{x}})^2=36\Rightarrow \frac{(\cos{x})^{2}}{(\sin{x})^{2}}=\frac{36}{1} \Rightarrow \frac{(\cos{x})^{2}+(\sin{x})^{2}}{(\sin{x})^{2}}=\frac{37}{1}\Rightarrow \frac{1}{(\sin{x})^{2}}=\frac{37}{1}\Rightarrow \sin{x}^{2}=\frac{1}{37} [/tex]
