Question

${\cos }^{2}30°{\cos }^{2}45°+4{\sec }^{2}60°+\frac{1}{2}{\cos }^{2}90°-2{\tan }^{2}60°=?$
(a) $\frac{73}{8}$
(b) $\frac{75}{8}$
(c) $\frac{81}{8}$
(d) $\frac{83}{8}$

Answer 1

(d) $\frac{83}{8}$

$$\begin{gathered} \left({\cos }^2{30}^{\mathrm{o}}{\cos }^2{45}^{\mathrm{o}}+4{\sec }^2{60}^{\mathrm{o}}+\frac{1}{2}{\cos }^2{90}^{\mathrm{o}}-2{\tan }^2{60}^{\mathrm{o}}\right) \\ =\left[{\left(\frac{\sqrt{3}}{2}\right)}^2\times {\left(\frac{1}{\sqrt{2}}\right)}^2+4\times {\left(2\right)}^2+\frac{1}{2}\times {\left(0\right)}^2-2\times {\left(\sqrt{3}\right)}^2\right] \\ =\left[\left({\displaystyle \frac{3}{4}}\times {\displaystyle \frac{1}{2}}\right)+16-6\right] \\ =\left[\frac{3}{8}+10\right] \\ =\frac{3+80}{8}=\frac{83}{8} \end{gathered}$$