Rút gọn biểu thức P = sin(a + 2023/4 pi 4) sin(a − 2023/4 pi 4).

Chọn A

\(\begin{array}{l}P = \sin \left( {a + \frac{{{{2023}^4}\pi }}{4}} \right)\sin \left( {a - \frac{{{{2023}^4}\pi }}{4}} \right)\\ =  - \frac{1}{2}\left[ {\cos \left( {a + \frac{{{{2023}^4}\pi }}{4} + a - \frac{{{{2023}^4}\pi }}{4}} \right) - \cos \left( {a + \frac{{{{2023}^4}\pi }}{4} - a + \frac{{{{2023}^4}\pi }}{4}} \right)} \right]\\ =  - \frac{1}{2}\left[ {\cos \left( {2a} \right) - \cos \frac{{{{2023}^4}\pi }}{2}} \right] =  - \frac{1}{2}\cos 2\alpha \end{array}\)