Question

The value of the expression $\frac{4}{3}{\cot }^2{30}^{\circ }+3{\sin }^2{60}^{\circ }-2{cosec}^2{60}^{\circ }+\frac{3}{4}{\tan }^2{30}^{\circ }$ is

Answer 1

$\frac{4}{3}co{t}^{2}30°+3{\sin }^{2}60°-2cose{c}^{2}60°+\frac{3}{4}ta{n}^{2}30°$

$=\frac{4}{3}(\sqrt{3}{)}^2+3\times (\frac{\sqrt{3}}{2}{)}^2-2\times (\frac{2}{\sqrt{3}}{)}^2+\frac{3}{4}\times (\frac{1}{\sqrt{3}}{)}^2=\frac{4}{3}\times 3+3\times \frac{3}{4}-2\times \frac{4}{3}+\frac{3}{4}\times \frac{1}{3}=4+\frac{9}{4}-\frac{8}{3}+\frac{1}{4}=\frac{48+27-32+3}{12}=\frac{78-32}{12}=\frac{46}{12}=\frac{23}{6}=3.8333$