1. **State the problem:** Simplify the expression $$B = 3 \cos^2 x \cdot x \left(1 - 2 \tan^2 x - 9 \cos^2 x\right)$$. 2. **Recall trigonometric identities:** - $$\tan^2 x = \frac{\sin^2 x}{\cos^2 x}$$ - $$\sin^2 x + \cos^2 x = 1$$ 3. **Rewrite the expression inside the parentheses:** $$1 - 2 \tan^2 x - 9 \cos^2 x = 1 - 2 \frac{\sin^2 x}{\cos^2 x} - 9 \cos^2 x$$ 4. **Find a common denominator for the terms inside the parentheses:** $$= \frac{\cos^2 x}{\cos^2 x} - \frac{2 \sin^2 x}{\cos^2 x} - \frac{9 \cos^4 x}{\cos^2 x} = \frac{\cos^2 x - 2 \sin^2 x - 9 \cos^4 x}{\cos^2 x}$$ 5. **Substitute back into the original expression:** $$B = 3 \cos^2 x \cdot x \cdot \frac{\cos^2 x - 2 \sin^2 x - 9 \cos^4 x}{\cos^2 x}$$ 6. **Cancel common factors:** $$B = 3 x \cancel{\cos^2 x} \cdot \frac{\cos^2 x - 2 \sin^2 x - 9 \cos^4 x}{\cancel{\cos^2 x}} = 3 x \left(\cos^2 x - 2 \sin^2 x - 9 \cos^4 x\right)$$ 7. **Express $$\sin^2 x$$ as $$1 - \cos^2 x$$:** $$B = 3 x \left(\cos^2 x - 2 (1 - \cos^2 x) - 9 \cos^4 x\right)$$ 8. **Simplify inside the parentheses:** $$= 3 x \left(\cos^2 x - 2 + 2 \cos^2 x - 9 \cos^4 x\right) = 3 x \left(3 \cos^2 x - 2 - 9 \cos^4 x\right)$$ 9. **Rewrite the expression:** $$B = 3 x \left(-9 \cos^4 x + 3 \cos^2 x - 2\right)$$ This is the simplified form of the original expression. **Final answer:** $$B = 3 x \left(-9 \cos^4 x + 3 \cos^2 x - 2\right)$$