$$\left[\frac{4}{3} an^2 60° + 3\cos^2 30° - 2\sec^2 30° - \frac{3}{4}\cot^2 60° ight] \div \left[\sin 60° \cos 30° - \cos 60° \sin 30° ight]$$

Question

$$\left[\frac{4}{3}	an^2 60° + 3\cos^2 30° - 2\sec^2 30° - \frac{3}{4}\cot^2 60°ight] \div \left[\sin 60° \cos 30° - \cos 60° \sin 30°ight]$$

Accepted Answer

Known values: - $	an 60° = \sqrt{3}$, so $	an^2 60° = 3$ - $\cos 30° = \frac{\sqrt{3}}{2}$, so $\cos^2 30° = \frac{3}{4}$ - $\sec 30° = \frac{2}{\sqrt{3}}$, so $\sec^2 30° = \frac{4}{3}$ - $\cot 60° = \frac{1}{\sqrt{3}}$, so $\cot^2 60° = \frac{1}{3}$
**Numerator:**
$$\frac{4}{3}(3) + 3\left(\frac{3}{4}ight) - 2\left(\frac{4}{3}ight) - \frac{3}{4}\left(\frac{1}{3}ight)$$
$$= 4 + \frac{9}{4} - \frac{8}{3} - \frac{1}{4}$$
$$= 4 + \frac{8}{4} - \frac{8}{3} = 4 + 2 - \frac{8}{3} = 6 - \frac{8}{3} = \frac{18-8}{3} = \frac{10}{3}$$
**Denominator:**
$$\sin 60° \cos 30° - \cos 60° \sin 30° = \sin(60° - 30°) = \sin 30° = \frac{1}{2}$$
**Final Answer:**
$$\frac{10}{3} \div \frac{1}{2} = \frac{10}{3} 	imes 2 = \frac{20}{3} = 6\frac{2}{3}$$

Answer

Answer

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