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Prove that: 2cospi/(13)cos(9pi)/(13)+cos...

Prove that: `2cos``pi/(13)``cos``(9pi)/(13)``+cos``(3pi)/(13)``+cos``(5pi)/(13)=0`

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To prove the equation: \[ 2 \cos\left(\frac{\pi}{13}\right) \cos\left(\frac{9\pi}{13}\right) + \cos\left(\frac{3\pi}{13}\right) + \cos\left(\frac{5\pi}{13}\right) = 0 \] we will follow these steps: ...
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Knowledge Check

  • 2"cos"(pi)/(13)"cos"(9pi)/(13)+"cos"(3pi)/(13)+"cos"(5pi)/(13) is equal to :

    A
    `-1`
    B
    0
    C
    1
    D
    `sqrt(3)//2`

  • The value of 2"cos"(pi)/(13)"cos"(9pi)/(13)+"cos"(3pi)/(13)+"cos"(5pi)/(13) is

    A
    `(1)/(2)`
    B
    0
    C
    `-(1)/(2)`
    D
    `(1)/(8)`

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    (i) cos20^(@) + cos100^(@) + cos 140^(@) =0 (ii) sin 50^(@) - sin 70^(@) + sin 10^(@) =0 (iii) 2 cos "" ( pi )/( 13) cos "" ( 9 pi )/( 13) + cos "" (3pi)/( 13) + cos "" ( 5pi )/( 13) =0

    Prove that: cos^(2)pi/8 + cos^(2)(3pi)/(8) + cos^(2)(5pi)/(8)+ cos^(2)(7pi)/(8)=2

    Prove that: (sin(8 pi))/(3)(cos(23 pi))/(6)+(cos(13 pi))/(3)(sin(35 pi))/(6)=(1)/(2)

    Prove that cos((pi)/(8))+cos((3 pi)/(8))+cos((5 pi)/(8))+cos((7 pi)/(8))=0

    Prove that (1+"cos" (pi)/10)(1+"cos"(3pi)/10)(1+"cos"(7pi)/10)(1+"cos"(9pi)/10)=1/16 .

    Hence deduce that cos(pi)/(9)cos(2 pi)/(9)cos(3 pi)/(9)cos(4 pi)/(9)=(1)/(16)

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