Every torus is contained in a Borel subgroup: let the torus act on the complete variety of Borel subgroups, or equivalently on a suitable quotient \(G/B\), and use the fixed-point theorem to find a Borel subgroup containing it. Thus two maximal tori \(T_1,T_2\) lie in Borel subgroups \(B_1,B_2\). Conjugacy of Borel subgroups lets us assume \(B_1=B_2=B\).

Inside the connected solvable group \(B\), maximal tori are conjugate by elements of \(R_u(B)\). Therefore \(T_1\) and \(T_2\) are conjugate in \(G\).