1. The problem is to prove or simplify an expression involving $\sin^2(x) \times \tan^2(x)$ and show how it equals the left side of the equation. 2. Recall the identity for tangent: $$\tan(x) = \frac{\sin(x)}{\cos(x)}$$ 3. Substitute $\tan^2(x)$ with $\left(\frac{\sin(x)}{\cos(x)}\right)^2$ in the expression: $$\sin^2(x) \times \tan^2(x) = \sin^2(x) \times \left(\frac{\sin(x)}{\cos(x)}\right)^2$$ 4. Simplify the right side: $$= \sin^2(x) \times \frac{\sin^2(x)}{\cos^2(x)} = \frac{\sin^4(x)}{\cos^2(x)}$$ 5. This shows the right side expression in terms of sine and cosine. 6. If the left side is given or known, compare it to this expression to verify equality or further simplify. 7. Important rule: When simplifying trigonometric expressions, always use fundamental identities like $\tan(x) = \frac{\sin(x)}{\cos(x)}$ and Pythagorean identities. This completes the explanation of how to transform the right side expression starting with $\sin^2(x) \times \tan^2(x)$ to a form that can be compared or equated to the left side.