Question

plzzz ans.....PROVE THE FOLLOWING

Answer 1

HELLO DEAR,

$\frac{ \sin \alpha }{ \cot \alpha + \cosec \alpha } \\ \\ = \frac{ \sin \alpha }{ \frac{ \cos \alpha }{ \sin\alpha } + \frac{1}{ \sin \alpha } } \\ \\ = \frac{ \sin \alpha }{ \frac{ \cos \alpha + 1 }{ \sin\alpha } } \\ \\ = \frac{ {sin \alpha }^{2} }{(1 + \cos \alpha )} \\ \\ = \frac{(1 - {cos}^{2} \alpha )}{(1 + cos \alpha )} \\ \\ = \frac{(1 - cos \alpha )(1 + cos \alpha )}{(1 + cos \alpha )} \\ \\ = (1 - cos \alpha )$

---------L.H.S.---------



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

-----------R.H.S.---------------


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Heya!!!


Here is your answer,



Hope it helps you,
Thank you.