The integrating factor of the differential equation cos x (d y)/(d x)…

$\cos x \frac{d y}{d x}+y \sin x=1$

$\Rightarrow \frac{d y}{d x}+y \tan x= \frac{1}{\cos x}$

So P(x) = tan x

So integrating factor = I.F = $e^{\int P(x) d x} = e^{\int \tan x d x}$

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

Option: 1