Given
#x=a(cosθ+cos2θ)....(1)#
#y=b(sinθ+sin2θ).....(2)#
From (1) and (2) we get
#x^2/a^2+y^2/b^2=(sintheta+sin2theta)^2+(costheta+cos2theta)^2#
#=>x^2/a^2+y^2/b^2=(sin^2theta+cos^2theta)+(sin^2 2theta+cos^2 2theta)+2(cos2thetacostheta+sin2thetasintheta)#
#=>x^2/a^2+y^2/b^2=1+1+2cos(2theta-theta)#
#=>x^2/a^2+y^2/b^2=2(1+costheta)....(3)#
Now by (1) we have
#x=a(cosθ+cos2θ)#
#=>x/a=2cos^2θ+costheta-1#
#=>x/a=2cos^2θ+2costheta-costheta-1#
#=>x/a=2cosθ(costheta+1)-(costheta+1)#
#=>x/a=(2cosθ-1)(costheta+1).....(4)#
Combining (3) and (4) we get
#=>x/a=(x^2/a^2+y^2/b^2-2-1)*1/2(x^2/a^2+y^2/b^2)#
#=>2x/a=(x^2/a^2+y^2/b^2-3)(x^2/a^2+y^2/b^2)#
#=>(x^2/a^2+y^2/b^2-3)(x^2/a^2+y^2/b^2)=(2x)/a#
