Cho \[{\rm{sin}}\left( {\rm{\alpha }} \right){\rm{ + cos}}\left( {\rm{\beta }} \right){\rm{ = }}\frac{{\rm{5}}}{{\rm{4}}}\], khi đó \(\sin \left( {2\alpha } \right)\)có giá trị bằng:

A. 30⁰

B. 90⁰

C. 60⁰

D. 40⁰

A. \[{\rm{cos}}\left( {{\rm{a + }}\frac{{\rm{\pi }}}{{\rm{3}}}} \right){\rm{ = cos}}\left( {\rm{a}} \right){\rm{ + }}\frac{{\rm{1}}}{{\rm{2}}}\]

B. \[{\rm{cos}}\left( {{\rm{a + }}\frac{{\rm{\pi }}}{{\rm{3}}}} \right){\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}{\rm{sin}}\left( {\rm{a}} \right) - \frac{{\sqrt {\rm{3}} }}{{\rm{2}}}{\rm{cos}}\left( {\rm{a}} \right)\]

C. \[{\rm{cos}}\left( {{\rm{a + }}\frac{{\rm{\pi }}}{{\rm{3}}}} \right){\rm{ = }}\frac{{\sqrt {\rm{3}} }}{{\rm{2}}}{\rm{sin}}\left( {\rm{a}} \right) - \frac{{\rm{1}}}{{\rm{2}}}{\rm{cos}}\left( {\rm{a}} \right)\]

D. \[{\rm{cos}}\left( {{\rm{a + }}\frac{{\rm{\pi }}}{{\rm{3}}}} \right){\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}{\rm{cos}}\left( {\rm{a}} \right) - \frac{{\sqrt {\rm{3}} }}{{\rm{2}}}{\rm{sin}}\left( {\rm{a}} \right)\]

A. \[{\rm{sin}}\left( {{\rm{B + C}}} \right){\rm{ = }} - {\rm{sin}}\left( {\rm{A}} \right)\]

B. \[{\rm{cos}}\left( {{\rm{B + C}}} \right){\rm{ = }} - {\rm{cos}}\left( {\rm{A}} \right)\]

C. \[{\rm{tan}}\left( {{\rm{B + C}}} \right){\rm{ = }} - {\rm{tan}}\left( {\rm{A}} \right)\]

D. \[{\rm{cot}}\left( {{\rm{B + C}}} \right){\rm{ = }} - {\rm{cot}}\left( {\rm{A}} \right)\]

A. \[{\rm{sin}}\left( {{\rm{2a}}} \right){\rm{ = 2sin}}\left( {\rm{a}} \right){\rm{cos}}\left( {\rm{a}} \right)\]

B. \[{\rm{sin}}\left( {{\rm{2a}}} \right){\rm{ = sin}}\left( {\rm{a}} \right){\rm{cos}}\left( {\rm{a}} \right)\]

C. \[{\rm{cos}}\left( {{\rm{2a}}} \right){\rm{ = co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{a}} \right) - {\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{a}} \right)\]

D. \[{\rm{cos}}\left( {{\rm{2a}}} \right){\rm{ = 1}} - {\rm{2si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{a}} \right)\]

A. \[{\rm{cos}}\left( {\rm{a}} \right){\rm{ + cos}}\left( {\rm{b}} \right){\rm{ = 2cos}}\left( {\frac{{{\rm{a + b}}}}{{\rm{2}}}} \right){\rm{cos}}\left( {\frac{{{\rm{a}} - {\rm{b}}}}{{\rm{2}}}} \right)\]

B. \[{\rm{cos}}\left( {\rm{a}} \right) - {\rm{cos}}\left( {\rm{b}} \right){\rm{ = }} - {\rm{2cos}}\left( {\frac{{{\rm{a + b}}}}{{\rm{2}}}} \right){\rm{cos}}\left( {\frac{{{\rm{a}} - {\rm{b}}}}{{\rm{2}}}} \right)\]

C. \[{\rm{sin}}\left( {\rm{a}} \right){\rm{ + sin}}\left( {\rm{b}} \right){\rm{ = 2sin}}\left( {\frac{{{\rm{a + b}}}}{{\rm{2}}}} \right){\rm{cos}}\left( {\frac{{{\rm{a}} - {\rm{b}}}}{{\rm{2}}}} \right)\]

D. \[{\rm{sin}}\left( {\rm{a}} \right) - {\rm{sin}}\left( {\rm{b}} \right){\rm{ = }} - {\rm{2sin}}\left( {\frac{{{\rm{a + b}}}}{{\rm{2}}}} \right){\rm{cos}}\left( {\frac{{{\rm{a}} - {\rm{b}}}}{{\rm{2}}}} \right)\]

A. \[{\rm{cos}}\left( {{\rm{2a}}} \right){\rm{ = si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{a}} \right) - {\rm{co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{a}} \right)\]

B. \[{\rm{cos}}\left( {{\rm{2a}}} \right){\rm{ = 1}} - {\rm{2co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{a}} \right)\]

C. \[{\rm{co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{a}} \right){\rm{ + si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{a}} \right){\rm{ = 1}}\]

D. \[{\rm{co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{a}} \right) - {\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{a}} \right){\rm{ = 1}}\]

A. S = 17

B. \[{\rm{S = }}\frac{{{\rm{17}}}}{{\rm{2}}}\]

C. S = 1

D. S = 0