$\text{ The solution of }\cos \mathrm{y}+(\mathrm{x}\text{ siny }-1)\frac{\mathrm{dy}}{\mathrm{dx}}=0\text{ is xsecy }=\text{ Ptany }+\mathrm{c}\text{ then ' }{\mathrm{P}}^{\mathrm{\prime }}\text{ is }$

$\begin{array}{l}\frac{\mathrm{dx}}{\mathrm{dy}}+\mathrm{xtany}=\mathrm{secy}\\ \text{ I.F. }={\mathrm{e}}^{\int \text{ tany }}={\mathrm{e}}^{\log \sec y}=\text{ secy }\\ \text{ Solution of the differential equation is ysecy }=\int {\sec }^2\text{ ydy }=\text{ tany }+c\\ \therefore \mathrm{P}=1\end{array}$