1. **State the problem:** We need to evaluate the expression $$B = \frac{\sin\left(\frac{2\pi}{3}\right)}{\cos^2\left(-\frac{\pi}{3}\right)}$$ and simplify it. 2. **Recall important trigonometric values and rules:** - $$\sin\left(\frac{2\pi}{3}\right) = \sin\left(\pi - \frac{\pi}{3}\right) = \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$$ - $$\cos\left(-\frac{\pi}{3}\right) = \cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$$ because cosine is an even function. 3. **Substitute these values into the expression:** $$B = \frac{\frac{\sqrt{3}}{2}}{\left(\frac{1}{2}\right)^2}$$ 4. **Simplify the denominator:** $$\left(\frac{1}{2}\right)^2 = \frac{1}{4}$$ 5. **Rewrite the expression:** $$B = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{4}}$$ 6. **Divide by a fraction by multiplying by its reciprocal:** $$B = \frac{\sqrt{3}}{2} \times \frac{4}{1}$$ 7. **Multiply numerators and denominators:** $$B = \frac{\sqrt{3} \times 4}{2} = \frac{4\sqrt{3}}{2}$$ 8. **Simplify the fraction by canceling common factors:** $$B = \frac{\cancel{4}\sqrt{3}}{\cancel{2}} \times 2 = 2\sqrt{3}$$ **Final answer:** $$B = 2\sqrt{3}$$