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Să se calculeze cos75 -cos15


Răspuns :

GreenEyes71
Salut,

[tex]cos75^{\circ}-cos15^{\circ}=-2\cdot sin\left(\dfrac{75^{\circ}+15^{\circ}}{2}\right)\cdot sin\left(\dfrac{75^{\circ}-15^{\circ}}{2}\right)=\\\\=-2\cdot sin(45^{\circ})\cdot sin(30^{\circ})=-2\cdot\dfrac{\sqrt2}2\cdot\dfrac{1}2=-\dfrac{\sqrt2}2.[/tex]

Green eyes.
Rayzen
[tex]\cos75^\circ -\cos15 ^{\circ} = \cos(45^{\circ} +30^{\circ} )-\cos(45^{\circ} -30^{\circ} ) = \\ \\ = \cos45^{\circ} \cdot \cos30^{\circ} -\sin45^{\circ} \cdot \sin30^{\circ} - \\ -(\cos45^{\circ} \cdot \cos30^{\circ} +\sin45^{\circ} \cdot \sin30^{\circ} ) = \\ \\ = \dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\cdot \dfrac{1}{2}-\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2} -\dfrac{\sqrt2}{2}\cdot \dfrac{1}{2} = [/tex]

[tex] = \dfrac{\sqrt6-\sqrt2-\sqrt6-\sqrt2}{4} = \dfrac{-2\sqrt2}{4} = -\dfrac{\sqrt2}{2}[/tex]

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