Question

Simplify : $(1-\cos \theta )(1+\cos \theta )(1+{\cot }^2\theta )$

Answer 1

$(1-\cos \theta )(1+\cos \theta )(1+{\cot }^2\theta )$

$=\left[\right(1-\cos \theta \left)\right(1+\cos \theta \left)\right(1+{\cot }^2\theta \left)\right]$

$=(1-{\cos }^2\theta )(1+{\cot }^2\theta )$

$={\sin }^2\theta .{\text{cosec}}^2\theta ={\sin }^2\theta \cdot \frac{1}{{\sin }^2\theta }=1$