Question

tính B=cos\(\frac{\text{π}}{7}\)*cos\(\frac{3\text{π}}{7}\)*cos\(\frac{5\text{π}}{7}\)

Answer 1

\(B=cos\frac{\pi}{7}.cos\left(\pi-\frac{4\pi}{7}\right).cos\left(\pi-\frac{2\pi}{7}\right)\)

\(B=cos\frac{\pi}{7}.cos\frac{2\pi}{7}.cos\frac{4\pi}{7}\)

\(B.sin\frac{\pi}{7}=sin\frac{\pi}{7}.cos\frac{\pi}{7}.cos\frac{2\pi}{7}.cos\frac{4\pi}{7}\)

\(B.sin\frac{\pi}{7}=\frac{1}{2}sin\frac{2\pi}{7}.cos\frac{2\pi}{7}.cos\frac{4\pi}{7}\)

\(B.sin\frac{\pi}{7}=\frac{1}{4}sin\frac{4\pi}{7}.cos\frac{4\pi}{7}=\frac{1}{8}sin\frac{8\pi}{7}\)

\(B.sin\frac{\pi}{7}=\frac{1}{8}sin\left(\pi+\frac{\pi}{7}\right)=-\frac{1}{8}sin\frac{\pi}{7}\)

\(\Rightarrow B=-\frac{1}{8}\)