\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{P}{\left({n}\right)}{y}={Q}{\left({n}\right)}\)

\(\displaystyle{I}.{F}={e}^{{\int{p}{\left({x}\right)}{\left.{d}{x}\right.}}}\)

\(\displaystyle={e}^{{\int-{\cot{{x}}}{\left.{d}{x}\right.}}}\)

\(\displaystyle={e}^{{-{\ln{{\sin{{n}}}}}}}\)

\(\displaystyle={e}^{{{\ln{{\frac{{{1}}}{{{\sin{{n}}}}}}}}}}\)

\(\displaystyle{I}.{F}.={\frac{{{1}}}{{{\sin{{n}}}}}}\)

\(\displaystyle{y}{\left({I}.{F}.\right)}=\int{\left({I}.{F}.\right)}{Q}{\left({x}\right)}\)

\(\displaystyle{\frac{{{1}}}{{{\sin{{x}}}}}}{y}=\int{\left\lbrace{{\sin}^{{3}}{x}}\right\rbrace}{\left\lbrace{\sin{{x}}}\right\rbrace}{d}{n}\)

\(\displaystyle{\frac{{{y}}}{{{\sin{{x}}}}}}=\int{{\sin}^{{2}}{n}}{\left.{d}{x}\right.}\)

\(\displaystyle{\frac{{{y}}}{{{\sin{{x}}}}}}=\int{\frac{{{1}-{\cos{{2}}}{x}}}{{{2}}}}{\left.{d}{x}\right.}\)

\(\displaystyle{\frac{{{y}}}{{{\sin{{x}}}}}}=\int{\frac{{{1}}}{{{2}}}}{\left.{d}{x}\right.}-\int{\frac{{{\cos{{2}}}{x}}}{{{2}}}}{\left.{d}{x}\right.}\)

\(\displaystyle{\frac{{{y}}}{{{\sin{{x}}}}}}={\frac{{{x}}}{{{2}}}}-{\frac{{{{\sin}^{{2}}{n}}}}{{{4}}}}+{c}\)

\(\displaystyle{y}={\frac{{{2}{\sin{{x}}}{\sin{{x}}}-{\sin{{x}}}{\sin{{2}}}{x}}}{{{4}}}}+{c}\)

\(\displaystyle{I}.{F}={e}^{{\int{p}{\left({x}\right)}{\left.{d}{x}\right.}}}\)

\(\displaystyle={e}^{{\int-{\cot{{x}}}{\left.{d}{x}\right.}}}\)

\(\displaystyle={e}^{{-{\ln{{\sin{{n}}}}}}}\)

\(\displaystyle={e}^{{{\ln{{\frac{{{1}}}{{{\sin{{n}}}}}}}}}}\)

\(\displaystyle{I}.{F}.={\frac{{{1}}}{{{\sin{{n}}}}}}\)

\(\displaystyle{y}{\left({I}.{F}.\right)}=\int{\left({I}.{F}.\right)}{Q}{\left({x}\right)}\)

\(\displaystyle{\frac{{{1}}}{{{\sin{{x}}}}}}{y}=\int{\left\lbrace{{\sin}^{{3}}{x}}\right\rbrace}{\left\lbrace{\sin{{x}}}\right\rbrace}{d}{n}\)

\(\displaystyle{\frac{{{y}}}{{{\sin{{x}}}}}}=\int{{\sin}^{{2}}{n}}{\left.{d}{x}\right.}\)

\(\displaystyle{\frac{{{y}}}{{{\sin{{x}}}}}}=\int{\frac{{{1}-{\cos{{2}}}{x}}}{{{2}}}}{\left.{d}{x}\right.}\)

\(\displaystyle{\frac{{{y}}}{{{\sin{{x}}}}}}=\int{\frac{{{1}}}{{{2}}}}{\left.{d}{x}\right.}-\int{\frac{{{\cos{{2}}}{x}}}{{{2}}}}{\left.{d}{x}\right.}\)

\(\displaystyle{\frac{{{y}}}{{{\sin{{x}}}}}}={\frac{{{x}}}{{{2}}}}-{\frac{{{{\sin}^{{2}}{n}}}}{{{4}}}}+{c}\)

\(\displaystyle{y}={\frac{{{2}{\sin{{x}}}{\sin{{x}}}-{\sin{{x}}}{\sin{{2}}}{x}}}{{{4}}}}+{c}\)