Question

Find the value of $\frac{4}{3}ta{n}^2{60}^{\circ }+3co{s}^2{30}^{\circ }-2se{c}^2{30}^{\circ }-\frac{3}{4}co{t}^2{60}^{\circ }$

• A. $3\frac{1}{3}$
• B. $\frac{1}{3}$
• C. 3
• D. $2\frac{1}{3}$

Answer 1

The correct option is A

$3\frac{1}{3}$

$\frac{4}{3}ta{n}^2{60}^{\circ }+3co{s}^2{30}^{\circ }-2se{c}^2{30}^{\circ }-\frac{3}{4}co{t}^2{60}^{\circ }$

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

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

= $4+\frac{9}{4}-\frac{8}{3}-\frac{1}{4}$

= $4+\frac{9}{4}-\frac{8}{3}-\frac{1}{4}$

= $\frac{10}{3}$

= $3\frac{1}{3}$