Rút gọn biểu thức M = cos²($\frac{\pi}{4}$ + $\alpha$) – cos²($\frac{\pi}{4}$ – $\alpha$) 13/08/2021 Bởi Kinsley Rút gọn biểu thức M = cos²($\frac{\pi}{4}$ + $\alpha$) – cos²($\frac{\pi}{4}$ – $\alpha$)
$\begin{array}{l}M = {\cos ^2}\left( {\dfrac{\pi }{4} + \alpha } \right) – {\cos ^2}\left( {\dfrac{\pi }{4} – \alpha } \right)\\M = \left[ {\cos \left( {\dfrac{\pi }{4} + \alpha } \right) – \cos \left( {\dfrac{\pi }{4} – \alpha } \right)} \right]\left[ {\cos \left( {\dfrac{\pi }{4} + \alpha } \right) + \cos \left( {\dfrac{\pi }{4} – \alpha } \right)} \right]\\M = – 2\sin \dfrac{\pi }{4}\sin \alpha .2.\cos \dfrac{\pi }{4}\cos \alpha \\M = – \sin \dfrac{\pi }{2}\sin 2\alpha = – \sin 2\alpha \end{array}$ Bình luận
$\begin{array}{l}
M = {\cos ^2}\left( {\dfrac{\pi }{4} + \alpha } \right) – {\cos ^2}\left( {\dfrac{\pi }{4} – \alpha } \right)\\
M = \left[ {\cos \left( {\dfrac{\pi }{4} + \alpha } \right) – \cos \left( {\dfrac{\pi }{4} – \alpha } \right)} \right]\left[ {\cos \left( {\dfrac{\pi }{4} + \alpha } \right) + \cos \left( {\dfrac{\pi }{4} – \alpha } \right)} \right]\\
M = – 2\sin \dfrac{\pi }{4}\sin \alpha .2.\cos \dfrac{\pi }{4}\cos \alpha \\
M = – \sin \dfrac{\pi }{2}\sin 2\alpha = – \sin 2\alpha
\end{array}$