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Let f(n)(theta)= 2 sin . (theta)/(2) sin...

Let `f_(n)(theta)= 2 sin . (theta)/(2) sin. (3theta)/(2) + 2 sin.(theta)/(2) sin. (5theta)/(2) + 2sin. (theta)/(2) sin. (7 theta)/(2) + ... + 2 sin (2 n+1) (theta)/(2), n in N`,
then which of the following is/are correct ?

A

`f_(9)(pi/4)=(1)/(sqrt(2))`

B

`f_(n)((2pi)/(n))=0, n in N`

C

`f_(3)((2pi)/(7))=0`

D

`f_(9)(pi/4)=-(1)/(sqrt(2))`

Text Solution

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The correct Answer is:
A, B, C
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