If x/a cos@ +y/b sin@ = 1 and x/a sin@ -y/b cos@ = 1 prove that x2/a2+y2/b2 =2

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 !