Question

Find the value of, $\frac{4}{3}{\cot }^2{30}^o+{\cot }^2{60}^o-2{\csc }^2{60}^o-\frac{3}{4}{\tan }^2{30}^o$

• A. $10/3$
• B. $11/3$
• C. $4$
• D. $noneofthese$

Answer 1

The correct option is D $noneofthese$

$\frac{4}{3}{\cot }^{2}30+{\cot }^{2}60-2{csc}^{2}60-\frac{3}{4}{\tan }^{2}30$

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

$\Rightarrow 4+\frac{1}{3}-\frac{8}{3}-\frac{1}{4}$

$\Rightarrow \frac{15}{4}-\frac{7}{3}$

$=\frac{17}{12}$

None of these.