20 câu trắc nghiệm Toán 11 Chân trời sáng tạo Các công thức lượng giác có đáp án

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

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

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

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

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

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

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

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

B. \[{\rm{cos}}\left( {\rm{x}} \right){\rm{ = }} - \frac{2}{3}\]

C. \[{\rm{cos}}\left( {\rm{x}} \right){\rm{ = }}\frac{{{\rm{2}}\sqrt {\rm{2}} }}{{\rm{3}}}\]

D. \[{\rm{cos}}\left( {\rm{x}} \right){\rm{ = }} - \frac{{2\sqrt 2 }}{3}\]

A. 1

B. – 1

C. \[\frac{{11}}{{19}}\]

D. \[\frac{{19}}{{11}}\]

A. \[\frac{{16}}{9}\]

B. \[\frac{6}{9}\]

C. \[\frac{9}{{16}}\]

D. \(\frac{9}{6}\)

A. \[\frac{{\sqrt 3 }}{6} - \frac{{\sqrt 2 }}{2}\]

B. \[\frac{{\sqrt 3 }}{3} + \frac{1}{2}\]

C. \[\frac{{\sqrt 3 }}{3} - \frac{1}{2}\]

D. \[\frac{{\sqrt 3 }}{6} + \frac{{\sqrt 2 }}{2}\]

A. \[{\rm{P = 1 + 3co}}{{\rm{s}}^{\rm{2}}}\left( {{\rm{2x}}} \right)\]

B. \[{\rm{P = 1 + }}\frac{{\rm{3}}}{{\rm{4}}}{\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{2x}}} \right)\]

C. \[{\rm{P = 1}} - \frac{{\rm{3}}}{{\rm{4}}}{\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{2x}}} \right)\]

D. \[{\rm{P = 1}} - {\rm{3co}}{{\rm{s}}^{\rm{2}}}\left( {{\rm{2x}}} \right)\]

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

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

C. \[{\rm{C = tan}}\left( {{\rm{2a}}} \right)\]

D. \[{\rm{D = cot}}\left( {{\rm{2a}}} \right)\]

A. \[\frac{{\rm{\pi }}}{{\rm{3}}}\]

B. \[ - \frac{{\rm{\pi }}}{{\rm{3}}}\]

C. \[\frac{{\rm{\pi }}}{{\rm{4}}}\]

D. \( - \frac{{\rm{\pi }}}{{\rm{4}}}\)

A. \[\frac{{17\sqrt 2 }}{{26}}\]

B. \[ - \frac{{17\sqrt 2 }}{{26}}\]

C. \[\frac{{\sqrt 2 }}{{26}}\]

D. \[ - \frac{{\sqrt 2 }}{{26}}\]

A. \[{\rm{co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{\alpha }} \right)\]

B. \[{\rm{co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{\beta }} \right)\]

C. \[{\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{\alpha }} \right)\]

D. \[{\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{\beta }} \right)\]

A. – 1

B. 0

C. 1

D. \(\frac{{ - 1}}{2}\)

A. S = 17

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

C. S = 1

D. S = 0

A. \[\widehat A{\rm{ = }}\widehat B{\rm{ = }}\widehat C{\rm{ = 6}}{{\rm{0}}^{\rm{0}}}\]

B. \[\widehat A{\rm{ = 9}}{{\rm{0}}^0}{\rm{; }}\widehat B{\rm{ = 6}}{{\rm{0}}^{\rm{0}}};\,\,\widehat C{\rm{ = 3}}{{\rm{0}}^{\rm{0}}}\]

C. \[\widehat A{\rm{ = 9}}{{\rm{0}}^0}{\rm{; }}\widehat B{\rm{ = 3}}{{\rm{0}}^{\rm{0}}};\,\,\widehat C{\rm{ = 6}}{{\rm{0}}^{\rm{0}}}\]

D. \[\widehat A{\rm{ = 9}}{{\rm{0}}^0}{\rm{; }}\widehat B{\rm{ = 4}}{{\rm{5}}^{\rm{0}}};\,\,\widehat C{\rm{ = 45}}{{\rm{0}}^{\rm{0}}}\]

A. q

B. p

C. 0

D. 1

A. 30⁰

B. 90⁰

C. 60⁰

D. 40⁰