Ans:(A)

Explanation:

Given differential equation is $\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y} \tan \mathrm{x}=\sec \mathrm{x}$

Which is linear differential equation 

Here, P=tan x,  Q=sec x

$$\begin{gathered} \therefore \mathrm{I}.\mathrm{F}={\mathrm{e}}^{\int \tan \mathrm{x} \mathrm{dx}}={\mathrm{e}}^{\log \left|\sec \mathrm{x}\right|}=\sec \mathrm{x} \\ \mathrm{The} \mathrm{general} \mathrm{solution} \mathrm{is} \\ \mathrm{y}.\sec \mathrm{x}=\int \sec \mathrm{x}.\sec \mathrm{x} \mathrm{dx}+\mathrm{c} \\ \Rightarrow \mathrm{y}.\sec \mathrm{x}=\int {\sec }^2 \mathrm{x} \mathrm{dx}+\mathrm{c} \\ \Rightarrow \mathrm{y}.\sec \mathrm{x}=\tan \mathrm{x}+\mathrm{c} \end{gathered}$$