Question

Evaluate: $4{\sin }^{2}60+3{\tan }^{2}30-8\sin 45.\cos 45$

Answer 1

$=4\times {\left(\frac{\sqrt{3}}{2}\right)}^2+3\times {\left(\frac{1}{\sqrt{3}}\right)}^2-8\times \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}$

$=4\times \frac{3}{4}+3\times \frac{1}{3}-8\times \frac{1}{2}$

$=3+1-4=0$