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"cos"pi/7+"cos"(2pi)/7+"cos"(3pi)/7+"cos...

`"cos"pi/7+"cos"(2pi)/7+"cos"(3pi)/7+"cos"(4pi)/7+"cos"(5pi)/7+"cos"(6pi)/7 =`

A

0

B

`3/2`

C

`3/4`

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
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{:(,"Column-I",,"Column-II"),((A),cos 20^(0) + cos 80^(0) - sqrt(3) "cos" 50^(0),(p),-1),((B),cos 0^(0) + "cos" (pi)/(7) + "cos" (2pi)/(7) + "cos" (4pi)/(7) + "cos" (5pi)/(7) + "cos" (6 pi)/(7),(q),-(3)/(4)),((C),cos 20^(0) + cos 40^(0) + cos 60^(0) - 4 cos 10^(0) "cos" 20^(0)"cos" 30^(0),(r),1),((D),"cos" 20^(0) cos 100^(0) + cos 100^(0) "cos" 140^(0) - cos 140^(0) "cos" 200^(0),(s),0):}

Knowledge Check

  • "cos" (2pi)/(7)+"cos" (4pi)/(7)+"cos"(6pi)/(7)=

    A
    `(1)/(2)`
    B
    `-(1)/(2)`
    C
    0
    D
    1

  • If "cos"(pi)/(15) "cos"(2pi)/(15) "cos"(4pi)/(15) "cos"(5pi)/(15) "cos"(7pi)/(15) "cos"(30pi)/(15) =x, " then " (1)/(8x) =

    A
    4
    B
    `(1)/(4)`
    C
    8
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  • cos""(2pi)/(15) cos ""(4pi)/(15)""cos(8pi)/(15) cos""(16pi)/(15)=

    A
    `1//4`
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    `1//8`
    C
    `1//16`
    D
    `1//32`

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