The correct options are
B x=y−1y+1
C y=1+x1−x
D xy+x−y+1=0
x=secϕ−tanϕ and y=cosecϕ+cotϕ
⇒x=1−sinϕcosϕ,y=1+cosϕsinϕ
Multiplying, we get
xy=(1−sinϕ)(1+cosϕ)cosϕsinϕ
xy=1−sinϕ+cosϕ−cosϕsinϕcosϕsinϕ
⇒xy+1=1−sinϕ+cosϕ−sinϕcosϕ+sinϕcosϕcosϕsinϕ
=1−sinϕ+cosϕcosϕsinϕ
and x−y=(1−sinϕ)sinϕ−cosϕ(1+cosϕ)cosϕsinϕ
=sinϕ−sin2ϕ−cosϕ−cos2ϕcosϕsinϕ
=sinϕ−cosϕ−1cosϕsinϕ=−(xy+1)
Thus, xy+x−y+1=0
⇒x=y−1y+1 and y=1+x1−x.