I think u made a typo error.The RHS must be x/a.

Continuing with what asish has done,2x/a=cosk+cos2k and 2y/b=sink+sin2k,

Squaring and adding,we get,4x²/a²+4y²/b²=2+2cosk and x²/a²+y²/b²=(1+cosk)/2

Subtract 3 from eqn1 and multiply the above eqns,the RHS is 1/2(cosk+1)(2cosk-1)=1/2(2cos²k+cosk-1)=1/2(cosk+cos2k)=x/a