Question

sa se arate ca 2*(sin 75-sin15)=radical din 2

Answer 1

2(sin75°-sin15°)=√2
2*2 sin 75°-15°/2*cos75°+15°/2
4*sin60°/2*cos90°/2
4*sin30°*cos45°=4*1/2*√2/2 =√2

Answer 2

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