Question

evaluate ​​cos 45 / sec 30 + 1/ sec 60

Answer 1

$$\begin{gathered} \frac{\cos 45°}{\sec 30°}+\frac{1}{\sec 60°} \\ =\frac{{\displaystyle \frac{1}{\sqrt{2}}}}{{\displaystyle \frac{2}{\sqrt{3}}}}+\frac{1}{2} \\ =\frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2} \\ =\frac{\sqrt{3}+\sqrt{2}}{2\sqrt{2}} \\ =\frac{\sqrt{3}+\sqrt{2}}{2\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}} \\ =\frac{\sqrt{6}+2}{4} \end{gathered}$$