What is the value of (1 + cot²θ)(1 - cos²θ).

Solution (By Examveda Team)

$$\eqalign{ & \left( {1 + {{\cot }^2}\theta } \right)\left( {1 - {{\cos }^2}\theta } \right) \cr & = \left( {1 + \frac{{{{\cos }^2}\theta }}{{{{\sin }^2}\theta }}} \right){\sin ^2}\theta \cr & = \left( {\frac{{{{\sin }^2}\theta + {{\cos }^2}\theta }}{{{{\sin }^2}\theta }}} \right){\sin ^2}\theta \cr & = 1 \cr} $$