Đơn giản biểu thức

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Đơn giản biểu thức \(C = {\rm{cos}}\left( {\frac{{3\pi }}{2} - a} \right) - {\rm{sin}}\left( {\frac{{3\pi }}{2} - a} \right) + {\rm{cos}}\left( {a - \frac{{7\pi }}{2}} \right) - {\rm{sin}}\left( {a - \frac{{7\pi }}{2}} \right)\)

\(2{\rm{sin}}a\).

\( - 2{\rm{sin}}a\).

\(2{\rm{cos}}a\).

\( - 2{\rm{cos}}a\).

Giải thích

Chọn B

\[\begin{array}{l}C = {\rm{cos}}\left( {\frac{{3\pi }}{2} - a} \right) - {\rm{sin}}\left( {\frac{{3\pi }}{2} - a} \right) + {\rm{cos}}\left( {a - \frac{{7\pi }}{2}} \right) - {\rm{sin}}\left( {a - \frac{{7\pi }}{2}} \right)\\ = {\rm{cos}}\frac{{3\pi }}{2}{\rm{cos}}a + {\rm{sin}}\frac{{3\pi }}{2}{\rm{sin}}a - \left( {{\rm{sin}}\frac{{3\pi }}{2}{\rm{cos}}a - {\rm{cos}}\frac{{3\pi }}{2}{\rm{sin}}a} \right)\\ + {\rm{cos}}a{\rm{cos}}\frac{{7\pi }}{2} + {\rm{sin}}a{\rm{sin}}\frac{{7\pi }}{2} - \left( {{\rm{sin}}a{\rm{cos}}\frac{{7\pi }}{2} - \cos a{\rm{sin}}\frac{{7\pi }}{2}} \right)\\ = 0.{\rm{cos}}a - {\rm{sin}}a - \left( { - {\rm{cos}}a - 0.{\rm{sin}}a} \right) + 0.{\rm{cos}}a - {\rm{sin}}a - \left( {{\rm{sin}}a.0 + \cos a} \right)\\ = - {\rm{sin}}a + {\rm{cos}}a - {\rm{sin}}a - {\rm{cos}}a = - 2\sin a\end{array}\]