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3.Trigonometrical Ratios, Functions and Identities
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The value of $\cos \,\frac{\pi }{7}\,\cos \,\frac{{2\pi }}{7}\,\cos \,\frac{{3\pi }}{7}$ is
A
$1/8$
B
$-1/8$
C
$1$
D
$0$
Solution
$\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7}$
$=\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \left(\pi-\frac{4 \pi}{7}\right)$
$=-\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}$
$=-\left[\frac{\sin \left(2^{3} \cdot \frac{\pi}{7}\right)}{2^{3} \sin \frac{\pi}{7}}\right]$
$=-\frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}=\frac{1}{8}$
Standard 11
Mathematics
