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Let f(x) = ax^2 + bx + c where a,b,c are...

Let `f(x) = ax^2 + bx + c` where `a,b,c` are integers. If `sin\ pi/7 * sin\ (3pi)/7 + sin\ (3pi)/7 * sin\ (5pi)/7 + sin\ (5pi)/7 * sin\ (pi)/7=f(cos\ (pi)/7)`. then find the value of `f(2):`

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Prove that: sinpi/7+sin(2pi)/(7) + sin(8pi)/7 + sin(9pi)/7=0

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Knowledge Check

  • The value of sin pi/16 sin (3 pi)/16 sin (5pi)/16 sin (7pi)/16 is :

    A
    `sqrt2/16`
    B
    `1/8`
    C
    `1/16`
    D
    `sqrt2/32`

  • The value of sin pi/16 sin (3 pi)/16 sin (5pi)/16 sin (7pi)/16 is :

    A
    `sqrt2/16`
    B
    `1/8`
    C
    `1/16`
    D
    `sqrt2/32`

  • The value of sin"" ( pi )/(7 ) +sin"" ( 2pi )/( 7 ) + sin "" ( 3pi )/(7) is

    A
    `cot "" ( pi )/(14)`
    B
    `(1)/( 2) cot "" ( pi )/( 14)`
    C
    `tan "" ( pi )/( 14)`
    D
    `(1)/( 2) tan "" ( pi )/( 14)`

    • Similar Questions

    Explore conceptually related problems

    The value of 2 sin (pi/8) sin((2pi)/8) sin((3pi)/8) sin ((5pi)/8) sin ((6pi)/8) sin((7pi)/8) is :

    sin(pi)/(4)*sin(3 pi)/(4)*sin(5 pi)/(4)*sin(7 pi)/(4)=

    sin ((pi) / (18)) * sin (5 (pi) / (18)) * sin (7 (pi) / (18))

    sin ((pi) / (7)) sin ((2 pi) / (7)) sin ((3 pi) / (7))

    sin""(pi)/(14)sin"" ( 3pi )/( 14)sin"" ( 5pi)/( 14)sin"" ( 7pi)/(14)

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