Question

$\frac{{\sec }^{2}54°-{\cot }^{2}36°}{{\mathrm{cosec}}^{2}57°-{\tan }^{2}33°}+2{\sin }^{2}38°{\sec }^{2}52°-{\sin }^{2}45°$

Answer 1

$$\begin{gathered} \begin{array}{l}\frac{{\sec }^2{54}^0-{\cot }^2{36}^0}{\cos {\text{ec}}^2{57}^0-{\tan }^2{33}^0}+2{\sin }^2{38}^0{\sec }^2{52}^0-{\sin }^2{45}^0\\ \end{array} \\ \begin{array}{l}\text{=}\frac{{\sec }^2{54}^0-{\cot }^2({90}^0-{54}^0)}{\cos {\text{ec}}^2{57}^0-{\tan }^2({90}^0-{57}^0)}+2{\sin }^2{38}^0{\sec }^2({90}^0-{38}^0)-{\left(\frac{1}{\sqrt{2}}\right)}^2\\ \end{array} \\ \begin{array}{l}=\frac{{\sec }^2{54}^0-{\tan }^2{54}^0}{\cos {\text{ec}}^2{57}^0-{\cot }^2{57}^0}+2{\sin }^2{38}^0\cos {\text{ec}}^2{38}^0-\frac{1}{2}\\ \end{array} \\ \begin{array}{l}{\text{=1+2sin}}^2{38}^0\frac{1}{{\sin }^2{38}^0}-\frac{1}{2}\\ \end{array} \\ \begin{array}{l}\text{=1+2}-\frac{1}{2}\\ \\ \end{array} \\ \begin{array}{l}\text{=3}-\frac{1}{2}\\ \end{array} \\ =\frac{5}{2} \end{gathered}$$