cos(a+b)=cosacosb−sinasinb\cos(a + b) = \cos a \cos b - \sin a \sin bcos(a+b)=cosacosb−sinasinb
cos75∘=cos(30+45)=(cos30)(cos45)−(sin30)(sin45)\cos75^{\circ} = \cos(30 + 45) = (\cos30)(\cos45) - (\sin30)(\sin45)cos75∘=cos(30+45)=(cos30)(cos45)−(sin30)(sin45)
= (32×22)−(12×22)\left(\frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}\right) - \left(\frac{1}{2} \times \frac{\sqrt{2}}{2}\right)(23×22)−(21×22)
= 6−24\frac{\sqrt{6} - \sqrt{2}}{4}46−2
= 2(3−1)4\frac{\sqrt{2}(\sqrt{3} - 1)}{4}42(3−1)
