Consider a flat plate with chord length \(c\) at an angle of attack \(\alpha\) to a supersonic free stream of Mach number \(M_{\infty}\). Let \(L\) and \(D\) be the lift and drag per unit span, respectively, and \(S\) be the planform area of the plate per unit span, \(S=c(1)\). Using linearized theory, derive the following expressions for the lift and drag coefficients (where \(C_{L} \equiv L / \frac{1}{2} ho_{\infty} V_{\infty}^{2} S\) and \(C_{D} \equiv D / \frac{1}{2} ho_{\infty} V_{\infty}^{2} S\) ):

a. \(C_{L}=\frac{4 \alpha}{\sqrt{M_{\infty}^{2}-1}}\)

b. \(C_{D}=\frac{4 \alpha^{2}}{\sqrt{M_{\infty}^{2}-1}}\)