Question

plzz ans.....PROVE THE FOLLOWING

Answer 1

HELLO DEAR,


$( \frac{1}{cos \alpha } - \frac{1}{sin \alpha } )(1 + \frac{sin \alpha }{cos \alpha } + \frac{cos \alpha }{sin \alpha } ) \\ \\ = ( \frac{sin \alpha - cos \alpha }{sin \alpha cos \alpha } )( \frac{sin \alpha cos \alpha + {(sin}^{2} \alpha + {cos}^{2} \alpha ) }{sin \alpha cos \alpha } ) \\ \\ = \frac{(sin \alpha - cos \alpha)(sin \alpha cos \alpha +{sin}^{2} \alpha + {cos}^{2} \alpha)}{sin ^{2} \alpha cos ^{2} \alpha } \\ \\ = \frac{ {sin}^{3} \alpha - {cos}^{3} \alpha }{sin ^{2} \alpha cos ^{2} \alpha} \\ \\ = \frac{ {sin}^{3} \alpha }{sin ^{2} \alpha cos ^{2} \alpha } - \frac{ {cos}^{3} \alpha }{sin ^{2} \alpha cos ^{2} \alpha} \\ \\ = tan \alpha sec \alpha - cot \alpha cosec \alpha$
I HOPE ITS HELP YOU DEAR,
THANKS