[tex]\text{Given: } sin(x) cot(x) cosec(x) = \sqrt{2}[/tex]
[tex]\text{Find: } cot(x)[/tex]
[tex]\text{Important identity: } \boxed{cosec(x) = \frac{1}{sin(x)}}[/tex]
[tex]sin(x) cot(x) cosec(x) = sin(x) cot(x) \frac{1}{sin(x)} = \sqrt{2}[/tex]
[tex]\therefore cot(x) = \sqrt{2}[/tex]
