Question

senx(cosecx-senx)/tanx=ctgx-1

Answer 1

Senx(1/sencillo -senx)/sen x/cosx =ctgx
Senx(1-sen2x/senx)/sen x/cosx =ctgx
Cos2x/senx/cosx/1=ctgx
Cosx/senx =ctgx
Ctgx = ctgx

Answer 2

$\sin(x) ( \frac{ \csc(x) - \sin(x) }{ \tan(x) }) = \cot(x) - 1 \\ \sin(x( \frac{ \frac{1}{ \sin(x) } - \sin(x) }{ \tan(x) } ) = \frac{ \cos(x) }{ \sin(x) } - 1\\ \frac{1 - { \sin(x) }^{2} }{ \frac{ \sin(x) }{ \cos(x) } } = \frac{ \cos(x) }{ \sin(x) } -1 \\ 1 - { \sin(x) }^{2} = { \cos(x ) }^{2} \\ \frac{ { \cos(x) }^{2} }{ \frac{ \sin(x) }{ \cos(x) } } = \frac{ \cos(x) }{ \sin(x) } - 1 \\ \frac{ { \cos(x) }^{3} }{ \sin(x) } = \frac{ \cos(x) }{ \sin(x) } - 1\\ { \cos(x) }^{2} = 1 \\ 1 - { \cos(x) }^{2} = 0 \\ { \sin(x ) }^{2} = 0$