\begin{array}{l} c o s (α + β) = s i n (90^{\circ} - (α + β)) \\ = s i n (90^{\circ} - α - β) \\ = s i n (90^{\circ} - α) c o s (β) - c o s (90^{\circ} - α) s i n (β) \\ = c o s (α) c o s (β) - s i n (α) s i n (β) \end{array}

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

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