Solution
= Solution
Apply the normal-shock relations to $M_{1n}=M_1\sin\theta_1$. Tangential <velocity> continuity and mass conservation give
$$
\tan\theta_2=\tan\theta_1\frac{2+(\gamma-1)M_1^2\sin^2\theta_1}{(\gamma+1)M_1^2\sin^2\theta_1}.
$$
As $M_1\to\infty$, maximize $\theta_1-\theta_2$; with $k=(\gamma-1)/(\gamma+1)$ the optimum has $\tan^2\theta_1=1/k$, and the maximum deflection is $\arcsin(1/\gamma)$.