We know that aerodynamic drag is proportional to the square of the velocity of the incoming flow: $$D=kV^2.$$
If I decompose velocity into arbitrary orthogonal $x$-$y$ directions:$$V_x=V\cos\theta\\V_y=V\sin\theta$$ we have $$D_x=kV_x^2\\D_y=kV_y^2.$$
Now my total drag is $$D=\sqrt{D_x^2+D_y^2}=k\sqrt{V_x^4+V_y^4}\le k(V_x^2+V_y^2)=kV^2.$$
So what's wrong with my calculation, or my idea? Are there any physical concept that I misused?