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If theta=pi/(2^n+1) , prove that: 2^ncos...

If `theta=pi/(2^n+1)` , prove that: `2^ncosthetacos2thetacos2^2 cos2^(n-1)theta=1.`

A

1

B

`(1)/(2^(n))`

C

`2^(n)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`cos thetacos2 thetacos2^(2)theta...cos2^(n-1)theta`
`=(sin(2^(n)theta))/(2^(n)sintheta)=(sin(pi-theta))/(2^(n)sintheta)" "[because2^(n)theta=pi-theta]=(1)/(2^(n))`
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