First replace y with x, which was clearly an error in the question.
Multiply top and bottom by cosx: (1+sinx)/(1-sinx).
Now multiply top and bottom by 1+sinx: (1+sinx)^2/(1-sin^2(x))=(1+2sinx+sin^2(x))/cos^2(x).
The question has cosx in the denominator. We can see if this is right or wrong by substituting x=45 degrees, because we know cos45=sin45=√(1/2), secx=√2, tan45=1.
If the identity in the question is correct then
(√2+1)/(√2-1)=(1+√2+1/2)√2=√2+2+1/√2=2+3√2/2.
The left-hand side rationalises to (√2+1)^2=2+2√2+1=3+2√2 which doesn't match the right-hand side.
If the denominator is cos^2(x) as indicated in the solution then the right-hand side is
(1+√2+1/2)2=3+2√2 which matches the left-hand side.
Therefore (secx+tanx)/(secx-tanx)=(1+2sinx+sin^2(x))/cos^2(x).