Cho tam giác nhọn ABC. Đẳng thức sai trong các đẳng thức sau là:

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

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

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

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

Giải thích

\[{\rm{sin}}\left( {{\rm{B + C}}} \right){\rm{ = sin}}\left( {{\rm{180}} - {\rm{A}}} \right){\rm{ = sin}}\left( {\rm{A}} \right)\]

\[{\rm{cos}}\left( {{\rm{B + C}}} \right){\rm{ = cos}}\left( {{\rm{180}} - {\rm{A}}} \right){\rm{ = }} - {\rm{cos}}\left( {\rm{A}} \right)\]

\[{\rm{tan}}\left( {{\rm{B + C}}} \right){\rm{ = tan}}\left( {{\rm{180}} - {\rm{A}}} \right){\rm{ = }} - {\rm{tan}}\left( {\rm{A}} \right)\]

\[{\rm{cot}}\left( {{\rm{B + C}}} \right){\rm{ = cot}}\left( {{\rm{180}} - {\rm{A}}} \right){\rm{ = }} - {\rm{cot}}\left( {\rm{A}} \right)\]

Vậy đẳng thức sai là:\(\sin \left( {B + C} \right){\rm{ = }} - \sin \left( A \right)\)

Đáp án cần chọn là: A