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3.Trigonometrical Ratios, Functions and Identities
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$96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$ is equal to$......$.
A
$3$
B
$2$
C
$4$
D
$1$
(JEE MAIN-2023)
Solution
$P=96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$
$2 P \times \sin \frac{\pi}{33}=96 \times 2 \sin \frac{\pi}{33} \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$
$2 P \times \sin \frac{\pi}{33}=6 \times \sin \frac{32 \pi}{33}=6 \sin \frac{\pi}{33}$
$P=3$
Standard 11
Mathematics
