Question

proov cosx-sinx+1/cosx+sinx-1=cosecx+cotx

Answer 1

HELLO DEAR,


$\frac{ \cos(x) - \sin(x) + 1 }{ \cos(x) + \sin(x) - 1 } \\ = \frac{ \cos(x) + 1 - \sin(x) }{ \cos(x) -( 1 - \ \sin(x)) } \times \frac{ \cos(x) + 1 - \sin(x) }{ \cos(x) + ( 1 - \ \sin(x))} \\ > \frac{( \cos(x) + (1 - \sin(x) )^{2} }{ \cos^{2} (x) - (1 - \sin(x) ) ^{2} } \\ = > \frac{ { \cos}^{2}x + 1 + \sin(x) ^{2} - 2 \sin(x) + 2 \cos(x) (1 - \sin(x) )}{ { \cos}^{2} x - 1 - { \sin }^{2} x+ 2 \sin(x) } \\ = > \frac{2 - 2 \sin(x) + 2 \cos(x)( 1 - \sin(x) )}{ - 2 \sin ^{2} (x) + 2 \sin(x) } \\ = > \frac{2(1 - \sin(x) )(1 + \cos(x) )}{2 \sin(x)(1 - \sin(x) ) } \\ = > \frac{1 + \cos(x) }{ \sin(x) } \\ = > \cosec(x) + \cot(x)$
I HOPE ITS HELP YOU DEAR,
THANKS