Question

evaluate ( cosec²45 + sin 30 )(tan45 + sec²45) / sin²60 cos^​245

Answer 1

$$\begin{gathered} \frac{\left({\mathrm{cosec}}^{2}45°+\sin 30°\right)\left(\tan 45°+{\sec }^{2}45°\right)}{{\sin }^{2}60°.{\cos }^{2}45°} \\ =\frac{\left[{\left(\sqrt{2}\right)}^2+{\displaystyle \frac{1}{2}}\right]\left[1+{\left(\sqrt{2}\right)}^2\right]}{{\left({\displaystyle \frac{\sqrt{3}}{2}}\right)}^2\times {\left({\displaystyle \frac{1}{\sqrt{2}}}\right)}^2} \\ =\frac{\left(2+{\displaystyle \frac{1}{2}}\right)\left(1+2\right)}{{\displaystyle \frac{3}{4}}\times {\displaystyle \frac{1}{2}}} \\ =\frac{{\displaystyle \frac{5}{2}}\times 3}{{\displaystyle \frac{3}{8}}} \\ =\frac{15}{2}\times \frac{8}{3} \\ =20 \end{gathered}$$