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  4. Value of cos (π/33) cos (2 π/33) cos (4 π/33) cos (8 π/33) cos (16 π/33)

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Q. Value of $\cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$

Trigonometric Functions

Solution:

$\frac{\sin \frac{2^5 \pi}{33}}{2^5 \sin \frac{\pi}{33}}=\frac{\sin \frac{32 \pi}{33}}{32 \sin \frac{\pi}{33}}=\frac{\sin \left(\pi-\frac{\pi}{33}\right)}{32 \sin \frac{\pi}{33}}=\frac{\sin \frac{\pi}{33}}{32 \sin \frac{\pi}{33}}=\frac{1}{32}$