$${\begin {array} {l} cos(\alpha + \beta) = sin(90^\circ - (\alpha + \beta)) \\ = sin(90^\circ - \alpha - \beta) \\ = sin(90^\circ - \alpha)\, cos(\beta) - cos(90^\circ - \alpha)\, sin(\beta)\\ = cos(\alpha)\, cos(\beta) - sin(\alpha)\, sin(\beta) \end {array}}$$