The value of 2sin(π/8)sin(2π/8)sin(3π/8)sin(5π/8)sin(6π/8)sin(7π/8) is:

Question

The value of 2sin\(\left(\cfrac{\pi}{8}\right)\)sin\(\left(\cfrac{2\pi}{8}\right)\)sin\(\left(\cfrac{3\pi}{8}\right)\)sin\(\left(\cfrac{5\pi}{8}\right)\)sin\(\left(\cfrac{6\pi}{8}\right)\)sin\(\left(\cfrac{7\pi}{8}\right)\)

2sin(π/8)sin(2π/8)sin(3π/8)sin(5π/8)sin(6π/8)sin(7π/8) is:

(1) \(\cfrac{1}{4\sqrt{2}}\)

(2) \(\cfrac{1}{4}\)

(3) \(\cfrac{1}{8}\)

(4) \(\cfrac{1}{8\sqrt{2}}\)

Answer 1

Correct answer is: (3) \(\cfrac{1}{8}\)

 2sin\(\left(\cfrac{\pi}{8}\right)\)sin\(\left(\cfrac{2\pi}{8}\right)\)sin\(\left(\cfrac{3\pi}{8}\right)\)sin\(\left(\cfrac{5\pi}{8}\right)\)sin\(\left(\cfrac{6\pi}{8}\right)\)sin\(\left(\cfrac{7\pi}{8}\right)\)