Question

$\frac{\left({\tan }^{2}60°+4{\sin }^{2}45°+3{\sec }^{2}30°+5{\cos }^{2}90°\right)}{\left(\mathrm{cosec}30°+\sec 60°-{\cot }^{2}30°\right)}=?$
(a) $\frac{9}{7}$
(b) 9
(c) $\frac{7}{9}$
(d) 6

Answer 1

(b) 9


$$\begin{gathered} \frac{\left({\tan }^2{60}^{\mathrm{o}}+4{\sin }^2{45}^{\mathrm{o}}+3{\sec }^2{30}^{\mathrm{o}}+5{\cos }^2{90}^{\mathrm{o}}\right)}{\left(\mathrm{cosec}{30}^{\mathrm{o}}+\sec {60}^{\mathrm{o}}-{\cot }^2{30}^{\mathrm{o}}\right)} \\ =\frac{\left[{\left(\sqrt{3}\right)}^2+4\times {\left(\frac{1}{\sqrt{2}}\right)}^2+3\times {\left(\frac{2}{\sqrt{3}}\right)}^2+5\times {\left(0\right)}^2\right]}{\left[2+2-{\left(\sqrt{3}\right)}^2\right]} \\ =\frac{\left[3+2+4\right]}{\left[4-3\right]}=9 \end{gathered}$$