Question

please solve it quickly .it's from trigo6

Answer 1

${ \csc }^{2} \alpha \: (1 + \frac{1}{ \sec \alpha} )(1 - \frac{1}{ \sec \alpha} ) \\ = { \csc }^{2} \alpha \: (1 + \cos \alpha )(1 - \cos \alpha ) \\ = { \csc }^{2} \alpha \: (1 - { \cos }^{2} \alpha ) \\ = { \csc }^{2} \alpha \: \times { \sin }^{2} \alpha = 1$