Rút gọn biểu thức A dưới đây A = s i n ( x + 85 π 2 ) + c o s ( 2023 π + x ) + s i n 2 ( x + 33 π ) + s i n 2 ( x − 5 π 2 ) , ta được:

16/20

Rút gọn biểu thức A dưới đây\[{\rm{A = sin}}\left( {{\rm{x + }}\frac{{{\rm{85\pi }}}}{{\rm{2}}}} \right){\rm{ + cos}}\left( {{\rm{2023\pi + x}}} \right){\rm{ + si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{x + 33\pi }}} \right){\rm{ + si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{x}} - \frac{{{\rm{5\pi }}}}{{\rm{2}}}} \right)\], ta được:

sinx

−2

−1

Giải thích

\[{\rm{A = sin}}\left( {{\rm{x + }}\frac{{{\rm{85\pi }}}}{{\rm{2}}}} \right){\rm{ + cos}}\left( {{\rm{2023\pi + x}}} \right){\rm{ + si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{x + 33\pi }}} \right){\rm{ + si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{x}} - \frac{{{\rm{5\pi }}}}{{\rm{2}}}} \right)\]

\[{\rm{A = sin}}\left( {{\rm{x + 42\pi + }}\frac{\pi }{2}} \right){\rm{ + cos}}\left( {{\rm{2022\pi + \pi + x}}} \right){\rm{ + sin2}}\left( {{\rm{32\pi + \pi + x}}} \right){\rm{ + si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{x}} - {\rm{2\pi }} - \frac{\pi }{2}} \right)\]\[{\rm{A = sin}}\left( {{\rm{x + }}\frac{\pi }{2}} \right){\rm{ + cos}}\left( {{\rm{\pi + x}}} \right){\rm{ + si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{\pi + x}}} \right){\rm{ + si}}{{\rm{n}}^{\rm{2}}}\left( {{\rm{x}} - \frac{\pi }{2}} \right)\]

\[{\rm{A = cosx}} - {\rm{cosx + }}{\left( { - {\rm{sinx}}} \right)^{\rm{2}}}{\rm{ + }}{\left( { - {\rm{cosx}}} \right)^{\rm{2}}}{\rm{ = si}}{{\rm{n}}^{\rm{2}}}{\rm{x + co}}{{\rm{s}}^{\rm{2}}}{\rm{x = 1}}\]

Chọn đáp án C.

Đáp án cần chọn là: C