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Find the value of |{:(cos((2pi)/(63)),,c...

Find the value of `|{:(cos((2pi)/(63)),,cos((3pi)/(70)),,cos((4pi)/(77))),(cos((pi)/(72)),,cos((pi)/(40)),,cos((3pi)/(88))),(1,,cos((pi)/(90)),,cos((2pi)/(99))):}|`

Text Solution

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`Delta= |{:(cos((pi)/(7)-(pi)/(9)),,cos((pi)/(7)-(pi)/(10)),,cos((pi)/(7)-(pi)/(11))),(cos((pi)/(8)-(pi)/(9)),,cos((pi)/(8)-(pi)/(10)),,cos((pi)/(8)-(pi)/(11))),(cos((pi)/(9)-(pi)/(9)),,cos((pi)/(9)-(pi)/(10)),,cos((pi)/(9)-(pi)/(11))):}|`
`|{:(cos((pi)/(7)-(pi)/(9)),,cos((pi)/(7)-(pi)/(10)),,cos((pi)/(7)-(pi)/(11))),(cos((pi)/(8)-(pi)/(9)),,cos((pi)/(8)-(pi)/(10)),,cos((pi)/(8)-(pi)/(11))),(cos((pi)/(9)-(pi)/(9)),,cos((pi)/(9)-(pi)/(10)),,cos((pi)/(9)-(pi)/(11))):}|`
`=0`
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Knowledge Check

  • The value of |(cos.(2pi)/(63),cos.(3pi)/(70),cos.(4pi)/(77)),(cos.(pi)/(72),cos.(pi)/(40),cos.(3pi)/(88)),(1,cos.(pi)/(90),cos.(2pi)/(99))| is equal to

    A
    0
    B
    1
    C
    `2cos.(pi)/(9)`
    D
    `cos.(pi)/(11)`
  • The value of cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((14pi)/(15)), is

    A
    1
    B
    `1//2`
    C
    `1//4`
    D
    `1//16`
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