Answer:
Given differential equation is \[\frac{dy}{dx}+y\tan x-\sec x=0\] \[\frac{dy}{dx}+\tan xy=\sec x\] Which is of the form of \[\frac{dy}{dx}+Py=Q\] Here, \[P=\tan x\]and \[Q=\sec x\] Now, Integrating Factor \[(lF)={{e}^{\int{pdx}}}={{e}^{\int{\tan xdx}}}\] \[={{e}^{\log \,\,\,|\,\,\sec x|}}\,\,=\sec x\]
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