Variant 2. (2008 National Exam I for Science) If the line $\frac{x}{a}+\frac{y}{b}$ $=1$ passes through the point $M(\cos \alpha, \sin \alpha)$, then $(\quad)$
A. $a^{2}+b^{2} \leqslant 1$
B. $a^{2}+b^{2} \geqslant 1$
C. $\frac{1}{a^{2}}+\frac{1}{b^{2}} \leqslant 1$
D. $\frac{1}{a^{2}}+\frac{1}{b^{2}} \geqslant 1$
Parse: Substituting the coordinates of point $M$ into the line $\frac{x}{a}+\frac{y}{b}=1$ yields:
$$\begin{aligned}
& 1=\left(\frac{\cos \alpha}{a}+\frac{\sin \alpha}{b}\right)^{2}=\left(\cos \alpha \cdot \frac{1}{a}+\sin \alpha \cdot \frac{1}{b}\right)^{2} \\
\leqslant & \left(\cos ^{2} \alpha+\sin ^{2} \alpha\right)\left(\frac{1^{2}}{a^{2}}+\frac{1^{2}}{b^{2}}\right) \text {, so } \frac{1}{a^{2}}+\frac{1}{b^{2}} \geqslant 1 .
\end{aligned}$$