Question

The value of E = sin${}^2$ 60${}^0$ cos${}^2$ 45${}^0$ + 8 tan${}^2$ 60${}^0$ + $\frac{1}{4}$cot${}^2$ 60${}^0$ is

• A. 527/24
• B. 545/24
• C. 559/24
• D. 521/24
• E. 587/24

Answer 1

The correct option is E

587/24

$\begin{array}{c}E={\left(\frac{\sqrt{3}}{2}\right)}^2{\left(\frac{1}{\sqrt{2}}\right)}^2+8{\left(\sqrt{3}\right)}^2+\frac{1}{4}{\left(\frac{1}{\sqrt{3}}\right)}^2\\ =\frac{3}{4}\times \frac{1}{2}+8\times 3+\frac{1}{4}\times \frac{1}{3}\\ =\frac{3}{8}+24+\frac{1}{12}\\ =24\frac{11}{24}\end{array}$