Question

2tan²30°-sin²60°÷3cos²30°​

Answer 1

Step-by-step explanation:

$2 {tan}^{2} 30 \: - \: {sin}^{2} 60 \: \div 3 {cos}^{2} 30$

$\frac{2 \times {( \frac{1}{ \sqrt{3} } })^{2} - ( { \frac{ \sqrt{3} }{2} })^{2} }{3 \times ({ \frac{1}{2} })^{2} }$

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

$= \frac{ \frac{2}{3} - \frac{3}{4} }{ \frac{3}{4} }$

$= \frac{ \frac{8 - 9}{12} }{ \frac{3}{4} }$

$= - \frac{1}{12} \times \frac{4}{3}$

$= - \frac{1}{9}$