1. The problem is to understand and express \(\tan x\) squared, which is commonly written as \(\tan^2 x\). 2. The notation \(\tan^2 x\) means \((\tan x)^2\), which is the square of the tangent of \(x\). 3. The tangent function is defined as \(\tan x = \frac{\sin x}{\cos x}\). 4. Therefore, \(\tan^2 x = \left(\frac{\sin x}{\cos x}\right)^2 = \frac{\sin^2 x}{\cos^2 x}\). 5. This expression is useful in trigonometric identities and simplifications. 6. For example, using the Pythagorean identity \(\sin^2 x + \cos^2 x = 1\), we can write \(\tan^2 x = \frac{1 - \cos^2 x}{\cos^2 x} = \frac{1}{\cos^2 x} - 1 = \sec^2 x - 1\). 7. This is a key identity: \(\tan^2 x = \sec^2 x - 1\). Final answer: \(\tan^2 x = \frac{\sin^2 x}{\cos^2 x} = \sec^2 x - 1\).