Sin (x-y) = 1-cot x tan y/csc x sec y?

Question

NEED HELP! Please show me the steps to get to the answer. Thanks!
sin (x-y) = 1-cot x tan y/csc x sec y

Answer 1

given eqution is sin ( x - y ) =1 -cotxtany /cscxsecy

Right hand side    =1 -cotxtany /cscxsecy

                          =1 -(cosx /sinx)*(siny /cosy) /(1/sinx)*( 1/cosy)          ( since   cotx =cosx/sinx ,tany =siny /cosy ,cscx =1/sinx ,secy =1/cosy)

                         =((sinxcosy -cosxsiny) /sinxcosy )*sinxcosy

cancel commen sings

                         =sinxcosy -cosxsiny

                        =sin ( x - y)                  ( since sin (x -y) =sinxcosy - cosxsiny)

the solution is     sin ( x - y ) =1 -cotxtany /cscxsecy

Answer 2

given equation is sin( x - y ) =1 - cotx tany /cscx secy

Simplify the equation from right hand side 1 - cotx tany /cscx secy

Recall trignometric reciprocal functions cotx = cosx/sinx, csxx = 1/sinx and secy = 1/cosy

=1 -(cosx /sinx) * (siny /cosy) /(1/sinx)*( 1/cosy)

= ((sinxcosy -cosxsiny) /sinxcosy )*sinxcosy

=sinxcosy - cosxsiny

=sin (x - y)                  (Recall sin (x -y) =sinxcosy - cosxsiny)

sin (x - y) =1 -cotxtany /cscxsecy.