Trigonometry

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If cospΘ + cosqΘ = o. prove that the different values of Θ form two arithmetical progressions in which the common differences are 2π/p+q and 2π/p-q respectively.

  • Trigonometry -

    cos px = -cos qx

    cos px = cos ( pi - qx )

    px = n ( pi ) + / - qx

    taking the first case

    px = n ( pi ) + qx

    x ( p - q ) = n ( pi )

    x = n ( ? p i) / ( p - q )

    taking the second case we get

    x = n ( ? pi ) / ( p + q )

    We find the common difference is what is asked.

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