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  4. The value of cos (π/22) . cos (π/23 ) . ...... . cos (π/210) . sin (π/210) is :

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Q. The value of $\cos \frac{\pi}{2^{2}} .\cos \frac{\pi}{2^{3} } . ...... .\cos \frac{\pi}{2^{10}} .\sin \frac{\pi}{2^{10}} $ is :

JEE MainJEE Main 2019Trigonometric Functions

Solution:

$2\sin \frac{\pi}{2^{10}} \cos \frac{\pi}{2^{10}} .......\cos \frac{\pi}{2^{2}} $
$ \frac{1}{2^{9} }\sin \frac{\pi}{2} = \frac{1}{512} $