[tex]2\cdot (\sin75^{\circ}-\sin15^{\circ}) = 2\cdot 2\cdot \sin \dfrac{75^{\circ}-15^{\circ}}{2}\cdot \cos\dfrac{75^{\circ}+15^{\circ}}{2} = \\ \\ = 4\cdot \sin \dfrac{60^{\circ}}{2}\cdot\cos \dfrac{90^{\circ}}{2} = 4\cdot \sin 30^{\circ}\cdot \cos 45^{\circ} = 4\cdot \dfrac{1}{2}\cdot \dfrac{\sqrt2}{2} = \sqrt2 \\ \\ \\ \boxed{$M-am folosit de formula: $ $ $ \sin a-\sin b = 2\cdot \sin \dfrac{a-b}{2}\cdot \cos \dfrac{a+b}{2} }[/tex]
