Trigonometry hardest questions?

Question

if x/a.cosØ + y/b.sinØ = 1 and x/a.sinØ - y/b.cosØ = 1 then prova that x^2/a^2 + y^2/b^2 = 2
know have to squar them... but really confused....
pleasee help mee...????

Answer 1

((x/a)cosø+(y/b)sinø)^2=(x/a)^2(cosø)^2+(y/b)^2(sinø)^2+2(xy/ab)sinøcosø=1

((x/a)sinø-(y/b)cosø)^2=(x/a)^2(sinø)^2+(y/b)^2(cosø)^2-2(xy/ab)sinøcosø=1

Add these two equations together, remembering that cos^2+sin^2=1:

(x/a)^2+(y/b)^2=2 QED