The value of following is : $$\frac{{\sin \theta .\operatorname{cosec} \theta .\tan \theta .\cot \theta }}{{{{\sin }^2}\theta + {\text{co}}{{\text{s}}^2}\theta }}$$     ?

Solution (By Examveda Team)

$$\eqalign{ & = \frac{{\sin \theta .\operatorname{cosec} \theta .\tan \theta .\cot \theta }}{{{{\sin }^2}\theta + {\text{co}}{{\text{s}}^2}\theta }} \cr & = \frac{{\sin \theta \times \frac{1}{{\sin \theta }} \times \tan \theta \times \frac{1}{{\tan \theta }}}}{1} \cr & = 1 \cr} $$