Thu gọn biểu thức P = s i n 6 ( x ) + c o s 6 ( x )

11/20

Thu gọn biểu thức\[{\rm{P = si}}{{\rm{n}}^{\rm{6}}}\left( {\rm{x}} \right){\rm{ + co}}{{\rm{s}}^{\rm{6}}}\left( {\rm{x}} \right)\]

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

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

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

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

Giải thích

\[{\rm{P = si}}{{\rm{n}}^{\rm{6}}}\left( {\rm{x}} \right){\rm{ + co}}{{\rm{s}}^{\rm{6}}}\left( {\rm{x}} \right){\rm{ = }}{\left[ {{\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{x}} \right)} \right]^{\rm{3}}}{\rm{ + }}{\left[ {{\rm{co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{x}} \right)} \right]^{\rm{3}}}\]

\[{\rm{ = }}{\left[ {{\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{x}} \right){\rm{ + co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{x}} \right)} \right]^{\rm{3}}} - {\rm{3si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{x}} \right){\rm{co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{x}} \right)\left[ {{\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{x}} \right){\rm{ + co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{x}} \right)} \right]\]

\[{\rm{ = 1}} - {\rm{3si}}{{\rm{n}}^{\rm{2}}}\left( {\rm{x}} \right){\rm{co}}{{\rm{s}}^{\rm{2}}}\left( {\rm{x}} \right){\rm{ = 1}} - \frac{{\rm{3}}}{{\rm{4}}}{\left[ {{\rm{2sin}}\left( {\rm{x}} \right){\rm{cos}}\left( {\rm{x}} \right)} \right]^{\rm{2}}}{\rm{ = 1}} - \frac{{\rm{3}}}{{\rm{4}}}{\rm{si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{2x}}} \right)\]

Đáp án cần chọn là: C