How about this one?
r^2= sec^2(theta) - tan^2(theta)
Hello, cmr7!
Someone created this problem as a joke . . .
Write in rectangular form: .$\displaystyle r^2\:=\: \sec^2\!\theta - \tan^2\!\theta$
We're expected to know this identity: .$\displaystyle \sec^2\!A - \tan^2\!A \:=\:1$
. . and this conversion: .$\displaystyle r^2 \:=\:x^2+y^2$
So: .$\displaystyle r^2 \:=\:\sec^2\!\theta - \tan^2\!\theta\;\text{ becomes: }\:r^2 \:=\:1 \quad\Rightarrow\quad x^2+y^2 \:=\:1$