If x/a cos@ +y/b sin@ = 1 and x/a sin@ -y/b cos@ = 1 ....square both equations
[x/a cos@ +y/b sin@ ]^2= 1 and [x/a sin@ -y/b cos@]^2 = 1
(x/a)^2 cos^2@ + 2(x/a)(y/b)sin@cos@ + (y/b)^2 sin^2@ = 1 and
(x/a)^2 sin^2@ -2(x/a)(y/b)sin@cos@ + (y/b)^2cos^2@= 1
---------------------- add
(x/a)^2[ cos^2@ + sin^2@] + (y/b)^2[ sin^2@+ cos^2@] = 2
(x/a)^2 + (y/b)^2 = 2
Hoping this helps !
[x/a cos@ +y/b sin@ ]^2= 1 and [x/a sin@ -y/b cos@]^2 = 1
(x/a)^2 cos^2@ + 2(x/a)(y/b)sin@cos@ + (y/b)^2 sin^2@ = 1 and
(x/a)^2 sin^2@ -2(x/a)(y/b)sin@cos@ + (y/b)^2cos^2@= 1
---------------------- add
(x/a)^2[ cos^2@ + sin^2@] + (y/b)^2[ sin^2@+ cos^2@] = 2
(x/a)^2 + (y/b)^2 = 2
Hoping this helps !