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Prove that cosx+cos((2pi)/3 - x)+cos((2p...

Prove that `cosx+cos((2pi)/3 - x)+cos((2pi)/3+x)=0`

Answer

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Knowledge Check

  • The sum of the solutions in (0, 2pi) of the equation cos x cos ((pi)/(3)-x)cos((pi)/(3)+x)=(1)/(4) is

    A
    `pi`
    B
    `2pi`
    C
    `3pi`
    D
    `4pi`

  • The extreme values of cos x cos((2pi)/(3)+x)cos((2pi)/(3)-x) is

    A
    `-1//2,1//2`
    B
    `-1//3,1//3`
    C
    `-1//4,1//4`
    D
    `-1//5,1//5`

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    Prove that cos^2x+cos^2(x+pi/3)+cos^2(x-pi/3)=3/2 .

    Prove that: cos((3pi)/2+x)cos(2pi+x)[cot((3pi)/2-x)+cot(2pi+x)]=1

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