sinα+sinβ=2sinα+β2cosα−β2 sin\alpha + sin\beta = 2sin\frac{\alpha+\beta}{2} cos\frac{\alpha - \beta}{2}

    sinα−sinβ=2cosα+β2sinα−β2 sin\alpha - sin\beta = 2cos\frac{\alpha + \beta}{2}sin\frac{\alpha - \beta}{2}

    cosα+cosβ=2cosα+β2cosα−β2 cos\alpha + cos\beta = 2cos\frac{\alpha + \beta}{2} cos\frac{\alpha - \beta}{2}

    cosα−cosβ=−2sinα+β2sinα−β2 cos\alpha - cos\beta = -2sin\frac{\alpha+\beta}{2} sin\frac{\alpha - \beta}{2}