Mathematics

Problem

The two polar curves

r=3

and

r=2\sec\theta

bound a region for angles

-\tfrac{\pi}{4}<\theta<\tfrac{\pi}{4}

. Without computing any integrals, determine whether

r_{\text{outer}}^{2}-r_{\text{inner}}^{2}

is positive, negative, or zero on this interval, and briefly justify your answer.