Question

please give me answer fast i give u hint u rationalize denominater

Answer 1

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