The value of $\displaystyle \left( \text{cosec}\theta -\sin { \theta } \right) \left( \sec{ \theta }-\cos { \theta } \right) \left( \tan { \theta } +\cot { \theta } \right)$ is

The value of $(\text{cosec} \theta -\sin \theta)(\sec \theta -\cos \theta)(\tan \theta +\cot \theta)$ is

$\displaystyle \left( \frac { 1 }{ \sin { \theta } } -\sin { \theta } \right) \left( \frac { 1 }{ \cos { \theta } } -\cos { \theta } \right) \left( \frac { \sin { \theta } }{ \cos { \theta } } +\frac { \cos { \theta } }{ \sin { \theta } } \right)$

$\displaystyle =\left( \frac { 1-{ \sin }^{ 2 }\theta }{ \sin { \theta } } \right) \left( \frac { 1-{ \cos }^{ 2 }\theta }{ \cos { \theta } } \right) \left( \frac { 1 }{ \sin { \theta } .\cos { \theta } } \right)$

$\displaystyle =\frac { { \cos }^{ 2 }\theta \times { \sin }^{ 2 }\theta }{ { \sin }^{ 2 }\theta \times { \cos }^{ 2 }\theta }$

$=1$