2) \( \tan ^{2} x\left(1-\sin ^{2} x\right) \)

This expression can be further simplified using trigonometric identities. Specifically, we know that \( 1 - \sin^2 x = \cos^2 x \). Therefore, \( \tan^2 x(1 - \sin^2 x) \) can be rewritten as \( \tan^2 x \cdot \cos^2 x = \frac{\sin^2 x}{\cos^2 x} \cdot \cos^2 x = \sin^2 x \). So, the expression simplifies neatly to \( \sin^2 x \)! An interesting fact about the tangent function is that it's periodic with a period of \( \pi \). This means that for any angle \( x \), \( \tan(x + n\pi) = \tan x \) where \( n \) is any integer. This property is particularly useful when solving trigonometric equations or analyzing graphs. Keep this in mind as you delve into the world of tangents!