1. **State the problem:** Simplify the expression $$\frac{7\cos^2 x - 7}{\sin^2 x}$$. 2. **Use the Pythagorean identity:** Recall that $$\sin^2 x + \cos^2 x = 1$$, so $$\cos^2 x = 1 - \sin^2 x$$. 3. **Rewrite the numerator:** $$7\cos^2 x - 7 = 7(\cos^2 x - 1) = 7((1 - \sin^2 x) - 1) = 7(1 - \sin^2 x - 1) = 7(-\sin^2 x) = -7\sin^2 x$$. 4. **Substitute back into the expression:** $$\frac{-7\sin^2 x}{\sin^2 x}$$. 5. **Simplify by canceling $$\sin^2 x$$:** $$\frac{\cancel{-7\sin^2 x}}{\cancel{\sin^2 x}} = -7$$. 6. **Final answer:** $$-7$$. This simplification shows that the original expression is equal to $$-7$$ for all $$x$$ where $$\sin x \neq 0$$.