RM{f}}\left( {\rm{x}} \right) = {\rm{\;}}\left( {1 + {\rm{cos\;x}}} \right){\rm{SIN\;x}} = \sin {\rm{x}} + \frac{1}{2}.\sin 2{\rm{x}}\)For maximum or minimum we should have \({\rm{f'}}\left( {\rm{x}} \right) = 0\)\(\therefore \cos {\rm{x}} + \cos 2{\rm{x}} = 0\)\(2\cos \frac{{3{\rm{x}}}}{2}.\cos \frac{{\rm{x}}}{2} = 0\)\(\therefore \frac{{3{\rm{x}}}}{2} = \frac{{\left( {2{\rm{n}} + 1} \right){\rm{\pi }}}}{2}{\rm{\;}}\left( {{\rm{or}}} \right)\frac{{\rm{x}}}{2} = \frac{{\left( {2{\rm{n}} + 1} \right){\rm{\pi }}}}{2}\)\({\rm{x}} = \frac{{\left( {2{\rm{n}} + 1} \right){\rm{\pi }}}}{3}{\rm{\;or\;}}\left( {2{\rm{n}} + 1} \right){\rm{\pi }}\)For maximum VALUE we should have \({\rm{x}} = \frac{{\left( {2{\rm{n}} + 1} \right){\rm{\pi }}}}{3}{\rm{\;i}}.{\rm{e}}.\frac{{\rm{\pi }}}{3} \ldots .\) \({\rm{f}}\left( {\frac{{\rm{\pi }}}{3}} \right) = \frac{{\sqrt 3 }}{2} + \frac{1}{2}\left( {\frac{{\sqrt 3 }}{2}} \right) = \frac{{3\sqrt 3 }}{4}\)