1. The problem is to simplify the expression $$\frac{(\sin x)^2}{\cos x}$$. 2. Recall the Pythagorean identity: $$\sin^2 x + \cos^2 x = 1$$. 3. We can rewrite the numerator as $$\sin^2 x$$ and keep the denominator as $$\cos x$$. 4. The expression is already simplified as a fraction, but we can express it in terms of tangent and secant functions: $$\frac{\sin^2 x}{\cos x} = \frac{\sin x \cdot \sin x}{\cos x} = \sin x \cdot \frac{\sin x}{\cos x} = \sin x \cdot \tan x$$. 5. Therefore, the simplified form is: $$\sin x \cdot \tan x$$. This is a more compact and useful form for many applications.