- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
normal
$\cos \frac{\pi }{7}\cos \frac{{2\pi }}{7}\cos \frac{{3\pi }}{7} =$
A
$-\frac{1}{8}$
B
$\frac{1}{16}$
C
$\frac{1}{8}$
D
None
Solution
$\frac{1}{2 \sin \frac{\pi}{7}}\left[2 \sin \frac{\pi}{7} \cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{\pi}{7}\right]$
$\frac{1}{2 \times 2 \sin \frac{\pi}{7}}\left[2 \sin \frac{2 \pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7}\right]$
$\frac{1}{2.4\sin \left(\frac{\pi}{3}\right)}\left(2 \sin 4 \frac{\pi}{7} \cos \frac{3 \pi}{7}\right)$
$\frac{1}{8 \sin \left(\frac{\pi}{7}\right)}\left[\sin (\pi)+\sin \left(\frac{\pi}{7}\right)\right]$
$\frac{\sin (\pi / 7)}{8 \sin (\pi / 7)}=\frac{1}{8}$
Standard 11
Mathematics
