Question

given that cosA=1/2the value of 2secA/1+tan²A

Answer 1

$$\begin{gathered} \cos \mathrm{A}=\frac{1}{2} \\ \frac{2\sec \mathrm{A}}{1+{\tan }^2\mathrm{A}}=\frac{2\sec \mathrm{A}}{{\sec }^2\mathrm{A}}\left(\mathrm{since}1+{\tan }^2\mathrm{x}={\sec }^2\mathrm{x}\right) \\ =\frac{2}{\sec \mathrm{A}}=2\cos \mathrm{A} \\ =2\left(\frac{1}{2}\right)=1\mathrm{ANS}... \end{gathered}$$