The integrating factor of differential equation $\cos x \frac{dy}{dx} + y \sin x = 1$ is

$\sec x$

The correct answer is Option (3) → $\sec x$ ##

Given that, $\cos x \frac{dy}{dx} + y \sin x = 1$

On dividing both sides by $\cos x$, we get

$⇒\frac{dy}{dx} + y \tan x = \sec x \quad \left[ ∵\frac{\sin x}{\cos x} = \tan x, \frac{1}{\cos x} = \sec x \right]$

On comparing $\frac{dy}{dx} + Py = Q$

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

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

$= \sec x \quad [∵ e^{\log x} = x]$