The numbers $\sin x,$ $\cos x,$ $\tan x$ form a geometric sequence.  Find
\[\cos^3 x + \cos^2 x.\]
To form a geometric sequence, the ratio between any two consecutive terms must be constant. So, I can write $\frac{\cos x}{\sin x} = \frac{\tan x}{\cos x},$ or $\cos^2 x = \sin x \tan x.$ I can simplify this by using the identity $\tan x = \frac{\sin x}{\cos x},$ and get $\cos^3 x = \sin^2 x.$ So, I get $\cos^3 x + \cos^2 x = 1 - \cos^2 x + \cos^2 x = 1.$

