Tính tổng S các nghiệm trên đoạn \[\left[ { - {\rm{\pi ; \pi }}} \right]\]của phương trình \[\left( {{\rm{2sinx}} - {\rm{1}}} \right)\left( {{\rm{2sin2x + 1}}} \right){\rm{ = 3}} - {\rm{4co}}{{\rm{s}}^{\rm{2}}}{\rm{x}}\]

A. \[\left\{ {\frac{{\rm{\pi }}}{{\rm{4}}}{\rm{ + }}\frac{{{\rm{k\pi }}}}{{\rm{2}}}} \right\}\]

B. \[\left\{ {\frac{{{\rm{k\pi }}}}{{\rm{4}}}} \right\}\]

C. \[\left\{ {{\rm{k\pi ; }}\frac{{\rm{\pi }}}{{\rm{4}}}{\rm{ + }}\frac{{{\rm{k\pi }}}}{{\rm{2}}}} \right\}\]

D. \[\left\{ {{\rm{k\pi ; }}\frac{{\rm{\pi }}}{{\rm{4}}}{\rm{ + k\pi }}} \right\}\]

A. 29

B. 41

C. 34

D. 13

A. \[{\rm{x = \pm }}\frac{{{\rm{2\pi }}}}{{\rm{3}}}{\rm{ + k2\pi }}\]

B. \[{\rm{x = \pm }}\frac{{\rm{\pi }}}{{\rm{6}}}{\rm{ + k\pi }}\]

C. \[{\rm{x = \pm }}\frac{{\rm{\pi }}}{{\rm{3}}}{\rm{ + k2\pi }}\]

D. \[{\rm{x = \pm }}\frac{{\rm{\pi }}}{{\rm{6}}}{\rm{ + k2\pi }}\]

A. 2

B. 3

C. 5

D. 4

A. \(\left[ {\begin{array}{*{20}{c}}{{\rm{x = }}\frac{{\rm{\pi }}}{{{\rm{12}}}}{\rm{ + k2\pi }}}\\{{\rm{x = }}\frac{{{\rm{11\pi }}}}{{{\rm{12}}}}{\rm{ + }}l{\rm{2\pi }}}\end{array}} \right.\left( {k,l \in \mathbb{Z}} \right)\)

B. \(\left[ {\begin{array}{*{20}{c}}{{\rm{x = }}\frac{{\rm{\pi }}}{{{\rm{12}}}}{\rm{ + k2\pi }}}\\{{\rm{x = }} - \frac{{\rm{\pi }}}{{{\rm{12}}}}{\rm{ + k2\pi }}}\end{array}} \right.\left( {k \in \mathbb{Z}} \right)\)

C. \({\rm{x = }}\frac{{\rm{\pi }}}{{{\rm{12}}}}{\rm{ + k2\pi }}\left( {k \in \mathbb{Z}} \right)\)

D. \({\rm{x = }}\frac{{{\rm{11\pi }}}}{{{\rm{12}}}}{\rm{ + k2\pi }}\,\left( {k \in \mathbb{Z}} \right)\)

C. \[{\rm{x = }}\frac{{\rm{\pi }}}{{\rm{3}}}{\rm{ + k\pi }}\,\,\left( {{\rm{k}} \in \mathbb{Z}} \right)\]

A. \[{\rm{x}} \in \emptyset \]

B. \(\left[ {\begin{array}{*{20}{c}}{{\rm{x = arcsin}}\left( {\frac{{\rm{3}}}{{\rm{2}}}} \right){\rm{ + k2\pi }}}\\{{\rm{x = \pi }} - {\rm{arcsin}}\left( {\frac{{\rm{3}}}{{\rm{2}}}} \right){\rm{ + k2\pi }}}\end{array}} \right.\left( {k \in \mathbb{Z}} \right)\)

C. \(\left[ {\begin{array}{*{20}{c}}{{\rm{x = arcsin}}\left( {\frac{{\rm{3}}}{{\rm{2}}}} \right){\rm{ + k2\pi }}}\\{{\rm{x = }} - {\rm{arcsin}}\left( {\frac{{\rm{3}}}{{\rm{2}}}} \right){\rm{ + k2\pi }}}\end{array}} \right.\left( {k \in \mathbb{Z}} \right)\)

D. \(x \in \mathbb{R}\)