Răspuns:
Explicație pas cu pas:
sin 75°=sin (90°-15°)=cos15° cos 75°=cos(90°-15)°=sin 15°
sin 75°/sin 15°-cos 75°/cos 15°=cos15°/sin 15°-sin 15°/cos15°=
=(cos²15°-sin²15°)/sin 15° cos15°=2cos30°/sin 30°=2tg 30°=2√3/3
[tex]\mathrm{E} = \dfrac{\sin 75^{\circ}}{\sin 15^{\circ}} - \dfrac{\cos 75^{\circ}}{\cos 15^{\circ}}\\ \\ \Rightarrow \mathrm{E}\cdot \sin 15^{\circ}\cos 15^{\circ} = \sin 75^{\circ} \cos 15^{\circ} -\cos 75^{\circ} \sin 15^{\circ}\\ \\\Rightarrow \dfrac{1}{2}\cdot \mathrm{E}\cdot 2 \sin 15^{\circ}\cos 15^{\circ} =\sin(75^{\circ} - 15^{\circ})\\ \\ \Rightarrow \dfrac{1}{2}\cdot \mathrm{E}\cdot \sin (2\cdot 15)^{\circ} = \sin 60^{\circ}\\ \\ \Rightarrow \dfrac{1}{2}\cdot \mathrm{E}\cdot \sin 30^{\circ} = \sin 60^{\circ}\\ \\ \Rightarrow \mathrm{E} = 2\cdot \dfrac{\sin 60^{\circ}}{\sin 30^{\circ}}\\ \\\Rightarrow \mathrm{E} = 2\cdot \dfrac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\\ \\\Rightarrow \mathbf{E = 2\sqrt{3}}[/tex]
