Question

Prove that ( cosA- sinA+1)( cosA+ sin A-1)= cosecA+ cotA

Answer 1

HELLO DEAR,

i think your something mistake in your questions

right questions is like that

Prove that:- ( cosA- sinA+1) / ( cosA+ sin A-1)= cosecA+ cotA
$\frac{( \cos \alpha - \sin \alpha + 1) }{( \cos \alpha + \sin\alpha - 1) } \\ = > \frac{ \sin \alpha ( \cos \alpha - \sin \alpha + 1) }{ \sin \alpha ( \cos \alpha + \sin \alpha - 1) } \\ = > \frac{ \sin \alpha \times \cos \alpha - {sin}^{2} \alpha + sin \alpha }{\sin \alpha ( \cos \alpha + \sin \alpha - 1)} \\ = > \frac{sin \alpha \times cos \alpha - (1 - {cos}^{2} \alpha ) + sin \alpha }{\sin \alpha ( \cos \alpha + \sin \alpha - 1)} \\ = > \frac{sin \alpha \times cos \alpha + sin \alpha -( 1 - {cos} \alpha) ( 1 + cos \alpha ) }{\sin \alpha ( \cos \alpha + \sin \alpha - 1)} \\ = > \frac{ \sin \alpha(1 + \cos \alpha ) - ( 1 - {cos} \alpha) ( 1 + cos \alpha )}{\sin \alpha ( \cos \alpha + \sin \alpha - 1)} \\ = > \frac{(1 + cos \alpha )(sin \alpha - 1 + cos \alpha )}{\sin \alpha ( \cos \alpha + \sin \alpha - 1)} \\ = > \frac{1 + cos \alpha }{ \sin\alpha } \\ = > \frac{1}{ \sin \alpha } + \frac{ \cos \alpha }{ \sin \alpha } \\ = cosec \alpha + \cot \alpha$
I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hello...

Question :- Prove that ( cosA- sinA+1)( cosA+ sin A-1)= cosecA+ cotA