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Question

Mathematics Question on Trigonometric Functions

The value of cos⁡π22.cos⁡π23........cos⁡π210.sin⁡π210\cos \frac{\pi}{2^{2}} .\cos \frac{\pi}{2^{3} } . ...... .\cos \frac{\pi}{2^{10}} .\sin \frac{\pi}{2^{10}} is :

A

1256\frac{1}{256}

B

12\frac{1}{2}

C

1512\frac{1}{512}

D

11024\frac{1}{1024}

Answer

1512\frac{1}{512}

Explanation

Solution

2sin⁡π210cos⁡π210.......cos⁡π222\sin \frac{\pi}{2^{10}} \cos \frac{\pi}{2^{10}} .......\cos \frac{\pi}{2^{2}} 129sin⁡π2=1512\frac{1}{2^{9} }\sin \frac{\pi}{2} = \frac{1}{512}