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the value of cos((pi)/(2^2))cos((pi)/(2^...

the value of `cos((pi)/(2^2))``cos((pi)/(2^3))``cos((pi)/(2^4))` .....`cos((pi)/(2^(10)))``sin((pi)/(2^(10)))` is (a) `(1)/(1024)` (b) `(1)/(512)` (c) `(1)/(256)` (d) `(1)/(128)`

A

`(1)/(512)`

B

`(1)/(1024)`

C

`(1)/(2)`

D

`(1)/(256)`

Text Solution

Verified by Experts

The correct Answer is:
A
`"cos"(pi)/(2^(2))*"cos"(pi)/(2^(3))........"cos"(pi)/(2^(10))*"sin"(pi)/(2^(10))`
`=............. (2 xx "cos"(pi)/(2^(10))*"sin"(pi)/(2^(10)))/(2)`
`=............. (2 *"cos"(pi)/(2^(9))*"sin"(pi)/(2^(9)))/(2*2 )`|
`=............. ("cos"(pi)/(2^(2))*"sin"(pi)/(2^(2)))/(2^(8))=("sin"(pi)/(2))/(2^(9))=(1)/(512)`
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