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Show that "cos"(pi)/(15)"cos"(2pi)/(15)"...

Show that `"cos"(pi)/(15)"cos"(2pi)/(15)"cos"(3pi)/(15)"cos"(4pi)/(15)"cos"(5pi)/(15)"cos"(6pi)/(15)"cos"(7pi)/(15)=(1)/(128)`.

Answer

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Knowledge Check

  • (1+"cos"(pi)/8)(1+"cos"(3pi)/8)(1+"cos"(5pi)/8)(1+"cos"(7pi)/8)=

    A
    `1/8`
    B
    `1/2`
    C
    `1/(sqrt(3))`
    D
    `1/(sqrt(2))`
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