Biểu thức sin pi/4.sin pi/12. sin 7pi/12 bằng

* Hướng dẫn giải

$$\begin{gathered} \sin \left(\frac{\mathrm{\pi }}{12}\right).\sin \left(\frac{7\mathrm{\pi }}{12}\right)=\frac{1}{2}\left[\cos \left(\frac{\mathrm{\pi }}{12}-\frac{7\mathrm{\pi }}{12}\right)-\cos \left(\frac{\mathrm{\pi }}{12}+\frac{7\mathrm{\pi }}{12}\right)\right] \\ =\frac{1}{2}.\left[\cos \frac{-\mathrm{\pi }}{2}-\cos \frac{2\mathrm{\pi }}{3}\right]=\frac{1}{2}.\left(0-\frac{-1}{2}\right)=\frac{1}{4} \\ \Rightarrow \sin \left(\frac{\mathrm{\pi }}{4}\right).\sin \left(\frac{\mathrm{\pi }}{12}\right).\sin \left(\frac{7\mathrm{\pi }}{12}\right)=\frac{\sqrt{2}}{2}.\frac{1}{4}=\frac{\sqrt{2}}{8} \end{gathered}$$