The integrating factor of differential equation $\frac{dy}{dx} + y \tan x - \sec x = 0$ is

$\sec x$

The correct answer is Option (2) → $\sec x$ ##

Given that, $\frac{dy}{dx} + y \tan x - \sec x = 0$

$\Rightarrow \frac{dy}{dx} + y \tan x = \sec x$

Which is a linear differential equation.

On comparing it with the equation $\frac{dy}{dx} + Py = Q$, we get

Here, $P = \tan x, Q = \sec x$

$\text{I.F} = e^{\int P \, dx} = e^{\int \tan x \, dx}$

$= e^{(\log \sec x)}$

$= \sec x \quad [∵e^{\log x} = x]$